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

generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+20x^89+2x^90+4x^91+5x^92

The gray image is a linear code over GF(2) with n=696, k=5 and d=356.
This code was found by Heurico 1.16 in 0.453 seconds.