The generator matrix

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

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+98x^28+136x^29+364x^30+454x^31+821x^32+858x^33+1275x^34+1508x^35+1788x^36+2334x^37+2436x^38+2782x^39+2692x^40+2956x^41+2480x^42+2466x^43+2042x^44+1538x^45+1276x^46+860x^47+634x^48+336x^49+315x^50+114x^51+104x^52+32x^53+44x^54+8x^55+12x^56+2x^57+2x^58

The gray image is a linear code over GF(2) with n=80, k=15 and d=28.
This code was found by Heurico 1.16 in 80.5 seconds.