The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+59x^82+278x^83+245x^84+520x^85+295x^86+452x^87+258x^88+358x^89+231x^90+306x^91+171x^92+264x^93+108x^94+184x^95+55x^96+102x^97+61x^98+52x^99+33x^100+36x^101+9x^102+8x^103+2x^104+5x^106+3x^108

The gray image is a linear code over GF(2) with n=356, k=12 and d=164.
This code was found by Heurico 1.16 in 1.37 seconds.