The generator matrix
1 0 0 0 1 1 1 X 0 0 0 1 1 1 1 0 X 1 1 1 0 1 0 X X 1 0 1 X 1 1 0 1 0 X 1 0 0 X 1 1 1 1 1 X 0 1 1 1 0 0 X X X 1 1 X 1 1 1 1 1 0 0 0 1 1 0 X 0 1 1 1 X X 0 1 1 1 1 1
0 1 0 0 0 0 0 0 1 1 1 1 X+1 1 1 X 1 1 X 1 X 0 0 1 1 X+1 1 1 1 X 0 0 X 0 X X+1 1 1 1 X+1 X+1 0 X 1 1 1 X+1 X+1 X+1 0 0 1 1 1 X+1 1 0 1 1 X+1 X 0 X 1 0 X 1 1 0 0 1 1 X+1 1 1 1 1 X X 1 X+1
0 0 1 0 0 1 1 1 X 1 X+1 1 1 X 0 0 X 0 X+1 X+1 1 0 1 1 0 1 1 0 X 1 1 1 1 1 0 0 X X+1 X+1 1 X+1 X X+1 X 1 0 X X 0 1 1 0 0 X X+1 X 0 X X+1 X+1 X+1 X 1 X 1 X 0 X+1 0 1 X+1 X+1 X 1 X 1 0 X 0 0 X
0 0 0 1 1 1 0 1 1 X+1 X 0 1 X+1 X 1 1 1 X 0 X 0 X+1 X X 1 1 X 1 1 X+1 X+1 X+1 0 1 X 0 1 0 1 0 X+1 X X+1 X+1 1 X X X+1 X+1 1 0 X+1 1 1 X 1 1 X+1 X 1 X+1 0 X+1 0 0 1 X 1 0 X+1 0 X+1 0 0 X X+1 X 0 1 X+1
0 0 0 0 X 0 0 0 0 0 0 X X X X X X 0 0 0 X X X 0 X X X 0 0 X X 0 0 0 0 0 X X X X 0 X X X 0 0 X 0 0 0 X 0 X X 0 X X 0 0 X X 0 0 X 0 0 0 X X X X X X X 0 0 0 X X 0 0
0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X 0 X X X X X X X X X X X X X X 0 X X X 0 X X X X X X X 0 X X 0 0 X X 0 X X 0 X X 0 X X 0 X X X X X 0
0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X 0 X X X X 0 0 X X 0 0 X X 0 0 0 X X X 0 0 0 X 0 X X 0 0 X X X X X X 0 X X X X 0 X 0 X 0 X 0 X 0 X 0 0
generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+60x^72+106x^73+120x^74+142x^75+145x^76+136x^77+113x^78+134x^79+144x^80+104x^81+79x^82+102x^83+102x^84+78x^85+64x^86+76x^87+71x^88+52x^89+48x^90+44x^91+35x^92+26x^93+15x^94+12x^95+11x^96+10x^97+9x^98+6x^100+2x^103+1x^104
The gray image is a linear code over GF(2) with n=162, k=11 and d=72.
This code was found by Heurico 1.16 in 0.8 seconds.