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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+78x^83+169x^84+202x^85+286x^86+326x^87+307x^88+332x^89+298x^90+312x^91+317x^92+272x^93+270x^94+210x^95+215x^96+190x^97+89x^98+64x^99+55x^100+20x^101+10x^102+24x^103+13x^104+6x^105+4x^106+10x^107+10x^108+2x^109+2x^110+1x^114+1x^124

The gray image is a linear code over GF(2) with n=364, k=12 and d=166.
This code was found by Heurico 1.16 in 1.83 seconds.