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

generates a code of length 94 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+15x^82+22x^83+49x^84+82x^85+128x^86+102x^87+218x^88+98x^89+332x^90+120x^91+522x^92+88x^93+632x^94+88x^95+505x^96+120x^97+303x^98+98x^99+177x^100+102x^101+89x^102+82x^103+35x^104+22x^105+14x^106+16x^108+10x^110+7x^112+8x^114+4x^116+5x^118+1x^120+1x^144

The gray image is a linear code over GF(2) with n=376, k=12 and d=164.
This code was found by Heurico 1.16 in 2.82 seconds.