The generator matrix

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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+50x^81+99x^82+106x^83+142x^84+140x^85+226x^86+202x^87+304x^88+354x^89+283x^90+408x^91+331x^92+312x^93+254x^94+208x^95+169x^96+114x^97+101x^98+70x^99+56x^100+40x^101+35x^102+22x^103+12x^104+10x^105+21x^106+8x^107+7x^108+4x^109+3x^110+2x^112+1x^118+1x^142

The gray image is a linear code over GF(2) with n=364, k=12 and d=162.
This code was found by Heurico 1.16 in 5.8 seconds.