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

generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+42x^81+42x^82+54x^83+38x^84+144x^85+55x^86+1338x^87+41x^88+116x^89+46x^90+62x^91+13x^92+16x^93+16x^94+14x^95+2x^96+2x^97+4x^99+1x^102+1x^164

The gray image is a linear code over GF(2) with n=696, k=11 and d=324.
This code was found by Heurico 1.16 in 0.937 seconds.