The generator matrix

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

generates a code of length 88 over Z2[X]/(X^4) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+112x^83+614x^84+432x^85+64x^86+480x^87+695x^88+480x^89+64x^90+432x^91+600x^92+112x^93+7x^96+2x^116+1x^120

The gray image is a linear code over GF(2) with n=704, k=12 and d=332.
This code was found by Heurico 1.16 in 0.782 seconds.