The generator matrix

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

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+24x^36+40x^37+36x^38+34x^39+28x^40+34x^41+19x^42+8x^43+6x^44+2x^45+4x^46+6x^47+2x^48+2x^49+3x^50+2x^53+2x^54+3x^56

The gray image is a linear code over GF(2) with n=80, k=8 and d=36.
This code was found by Heurico 1.16 in 0.0117 seconds.