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

generates a code of length 93 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+68x^82+139x^84+16x^85+241x^86+32x^87+347x^88+128x^89+289x^90+224x^91+486x^92+224x^93+482x^94+224x^95+278x^96+128x^97+323x^98+32x^99+206x^100+16x^101+98x^102+57x^104+15x^106+14x^108+10x^110+4x^112+9x^114+3x^116+1x^118+1x^144

The gray image is a linear code over GF(2) with n=372, k=12 and d=164.
This code was found by Heurico 1.16 in 2.82 seconds.