The generator matrix

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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+2x^90+8x^91+3x^92+1x^94+1x^98

The gray image is a linear code over GF(2) with n=172, k=4 and d=90.
This code was found by Heurico 1.16 in 0.113 seconds.