The generator matrix

 1  0  1  1  1  0  1  1  X  1  1  X  1  1  0  1  1  0  1  1  X  1  1  X  1  1  0  1  1  0  1  1  X  1  1  X  1  1  1  1  1  1  1  1  X  X  0  0  0  X  0  X  1  1  1  1  0  X  1  1  1  1  X  X  0  X  X  0  0  0  X  X  X  0  1  1  1  1  1  1  1  1  X  X  0  0  0  X  1
 0  1  1  0 X+1  1  X X+1  1  X  1  1  0 X+1  1  0 X+1  1  X  1  1  X  1  1  0 X+1  1  0 X+1  1  X  1  1  X  1  1  0  0 X+1 X+1  X  X  1  1  0  X  X  0  1  1  1  1  0  X X+1  1  1  1  0  X X+1  1  0  X  X  0  X  X  0  1  1  0  X  X  0  0  X  X X+1 X+1  1  1  0  X  X  0  1  1  0
 0  0  X  X  0  X  X  X  X  0  0  0  0  0  X  X  X  0  X  X  X  0  0  0  0  0  X  X  X  0  X  X  X  0  0  0  0  X  0  X  X  0  X  0  X  X  X  X  0  0  X  X  0  0  0  0  X  X  X  X  X  X  0  0  0  X  X  X  X  0  0  0  0  0  0  X  X  0  0  X  X  0  X  X  X  X  0  0  0

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+4x^90+16x^91+6x^92+2x^94+1x^96+2x^98

The gray image is a linear code over GF(2) with n=178, k=5 and d=90.
This code was found by Heurico 1.16 in 0.133 seconds.