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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  1  1  1  1 X^3  1  X  1  1  1  1  1 X^2  1  1  X  X X^3  1  X  1 X^3+X^2 X^2  1  0 X^3  0
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^3+X^2+X X^3 X^3+X^2+X X^3+X^2  X  0 X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3 X^2+X X^3+X^2 X^3+X X^2 X^3+X X^3 X^2+X X^3+X^2  X X^3 X^3+X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^3+X X^2  0 X^2+X X^2 X^3+X X^3+X^2 X^3 X^3+X^2+X X^3+X^2+X  X X^3 X^3+X^2 X^3+X X^3+X^2+X X^3 X^3+X^2  X X^2 X^3 X^3+X X^3 X^3+X X^3+X^2 X^3+X X^3+X^2+X X^3+X^2+X X^3  X X^2+X X^2+X  X X^2 X^2  0 X^3+X  X  0  0 X^3+X X^2+X  X X^3+X^2+X X^3+X^2+X X^3+X^2+X  X  X X^2  X  X  X
 0  0 X^3+X^2  0 X^2 X^3 X^3  0 X^2  0 X^3+X^2 X^3+X^2 X^2 X^2 X^3 X^2 X^3  0 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^2 X^3  0 X^2 X^3+X^2 X^2 X^3  0  0  0 X^2 X^3+X^2  0  0  0  0 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^3  0 X^3 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3+X^2  0 X^2 X^3+X^2 X^2 X^2 X^3 X^3 X^3+X^2 X^3 X^3 X^3 X^3  0 X^2 X^3+X^2 X^3  0  0 X^3+X^2 X^3 X^3  0 X^2 X^3+X^2  0 X^3+X^2  0 X^2  0 X^3+X^2 X^3+X^2 X^2  0 X^3 X^3+X^2
 0  0  0 X^3+X^2  0  0  0 X^2 X^3 X^2 X^2 X^3+X^2  0 X^3+X^2 X^2 X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^3  0 X^3 X^2 X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3  0 X^3 X^3 X^3+X^2  0  0 X^3  0  0 X^2 X^3  0  0  0  0 X^3 X^2 X^3+X^2  0 X^3+X^2 X^2 X^3 X^2  0 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3  0 X^3+X^2  0  0 X^3  0 X^2 X^3+X^2  0 X^2 X^3 X^2 X^3+X^2
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+200x^83+92x^84+290x^85+232x^86+378x^87+723x^88+408x^89+688x^90+304x^91+230x^92+256x^93+40x^94+138x^95+33x^96+58x^97+4x^99+6x^100+10x^101+2x^104+2x^105+1x^152

The gray image is a linear code over GF(2) with n=712, k=12 and d=332.
This code was found by Heurico 1.16 in 121 seconds.