The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+72x^81+123x^82+270x^83+216x^84+444x^85+257x^86+386x^87+179x^88+296x^89+307x^90+366x^91+151x^92+382x^93+162x^94+228x^95+65x^96+70x^97+23x^98+18x^99+15x^100+14x^101+13x^102+10x^103+11x^104+2x^105+9x^106+2x^107+1x^108+2x^114+1x^116

The gray image is a linear code over GF(2) with n=356, k=12 and d=162.
This code was found by Heurico 1.16 in 1.76 seconds.