The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3  1  1 X^3+X^2+X  1 X^3+X^2  1  1 X^3+X  1  1  1  1 X^2  X  1  1  1  1 X^3  1 X^3+X^2+X  1  1  1 X^2  1  X  1 X^3  1 X^3+X^2+X  1  1 X^2  1  1  X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X^3+X^2+X  X X^3+X^2 X^3
 0  1 X+1 X^3+X^2+X X^3+X^2+1  1  X X+1  1 X^3+X^2 X^2+1  1 X^2+X+1  1 X^3  1  1 X^2+X X^3+X^2+X+1 X^3+1 X^3+X  1  1  X X^2 X^3+X+1 X^3+X^2+1  1 X^3  1 X^3+X^2+X X^2+X+1  1  1 X^2  1 X^3  1 X+1  1 X^2+1 X^3+X  1 X^2 X^3+1  1 X^2+X X^3+X^2+X+1 X^3+X^2 X^2+X  X X^3+X^2+X X^2+X  X X^3+X^2+X X^3  X X^2  0 X^3 X^3 X^2  0  X X^3+X+1 X^2+1 X^3+X+1 X^3+1 X^2+X X^3+X+1 X^2+X+1 X^2+X+1 X^2+1 X^3+X^2 X^2 X^2+X+1  1 X^2+X+1  1  1 X+1  0  1  1 X^3+X^2  X  1
 0  0 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3 X^2 X^2  0 X^3+X^2 X^3+X^2  0  0 X^3 X^3  0 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3  0 X^2 X^3+X^2 X^3  0 X^2 X^3+X^2  0 X^2 X^3  0 X^3+X^2 X^3  0 X^3  0 X^2 X^3+X^2 X^3  0 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^3+X^2
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 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+104x^83+184x^84+392x^85+319x^86+278x^87+206x^88+216x^89+122x^90+124x^91+56x^92+32x^93+5x^94+4x^95+1x^98+1x^106+2x^111+1x^128

The gray image is a linear code over GF(2) with n=696, k=11 and d=332.
This code was found by Heurico 1.16 in 0.828 seconds.