The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+344x^83+204x^84+536x^85+204x^86+626x^87+183x^88+460x^89+124x^90+406x^91+124x^92+272x^93+76x^94+182x^95+43x^96+124x^97+22x^98+50x^99+20x^100+40x^101+20x^102+16x^103+1x^104+8x^105+2x^106+8x^107

The gray image is a linear code over GF(2) with n=356, k=12 and d=166.
This code was found by Heurico 1.16 in 93 seconds.