The generator matrix

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

generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+194x^83+742x^84+570x^85+706x^86+396x^87+426x^88+232x^89+254x^90+134x^91+208x^92+102x^93+46x^94+28x^95+45x^96+8x^97+2x^100+2x^106

The gray image is a linear code over GF(2) with n=696, k=12 and d=332.
This code was found by Heurico 1.16 in 4.37 seconds.