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

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

Homogenous weight enumerator: w(x)=1x^0+3x^88+54x^89+4x^90+2x^101

The gray image is a linear code over GF(2) with n=704, k=6 and d=352.
This code was found by Heurico 1.16 in 0.563 seconds.