The generator matrix

 1  0  0  1  1  1  0  1  X X^2  1  1 X^2+X  1  1 X^2  1  X  0  1  1  X  1  X  1  1  X  1  1  X  1  0  1  1  1  1  1  X  0  1  1  X  1  1 X^2+X X^2+X  1 X^2+X  1  1  1  1  0 X^2  0  1  1  1 X^2  1  1  1 X^2+X X^2  X  1  1  1 X^2+X  X  1  X X^2+X  X  1  X  1  1  0  1  X  1  1  1 X^2  1  1  1
 0  1  0  0  1  1  1  X  1 X^2+X X^2+X X^2+1  1 X+1 X^2  1 X^2+X+1  0  1 X+1 X^2 X^2+X X^2+X  1  X X^2+X+1  1  1 X^2+1  1  1  1 X^2+X  0 X^2+1 X^2+X  X  1  1 X^2+X+1  0  X X+1 X^2  1  1  X  X X^2+1 X^2+X X+1 X^2+X  X  1 X^2+X X^2+1  1 X+1  1  1 X^2+X+1  0  1 X^2  X  0  1 X^2  1  1  0  1  1  1 X^2+X+1  1  1  X  1 X^2+1 X^2 X+1 X^2 X^2  1 X+1 X^2  0
 0  0  1 X+1 X^2+X+1  0 X+1  1 X^2  1  0  1  1  0 X^2+1  X  1  1 X^2+1  X X^2+X  1 X^2+X+1 X^2+X+1  X X^2+X+1 X^2+X X^2+X  X X^2+X  1 X+1 X+1  X  0  1 X^2  0 X^2+1 X^2+X+1 X+1  1  1  1 X^2+X+1  X  X  1 X+1 X+1 X^2  X  1  1  1  1 X^2+X+1 X^2+X X^2 X^2+1 X^2+1  0 X+1  1  1 X^2+X  X X^2+X  1 X^2+X+1  1  1 X^2+1 X+1 X^2 X^2+X+1 X^2+X  X  0 X^2+X+1  1 X+1 X^2+1 X+1 X^2+1 X+1 X^2+X+1  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0
 0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+132x^81+160x^82+386x^83+294x^84+460x^85+276x^86+408x^87+253x^88+406x^89+189x^90+318x^91+136x^92+182x^93+104x^94+126x^95+63x^96+82x^97+27x^98+32x^99+14x^100+14x^101+11x^102+10x^103+7x^104+4x^105+1x^110

The gray image is a linear code over GF(2) with n=352, k=12 and d=162.
This code was found by Heurico 1.16 in 1.34 seconds.