The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  X  1  0  0  1  1  0  1  0  1  1  1  X  1  1  0  1  1  1  0  1  1  1  1  0  1  1  1
 0  1  0  0  0  0  0  0  0  1  1 X+1  0 X+1  1  1 X+1  X  0 X+1  X  X  1  1  1  X  0  1  X  1 X+1  0 X+1 X+1  0  0  1  X  0  0
 0  0  1  0  0  0  0  0  0  0  1 X+1  1  X  0 X+1 X+1 X+1  X  X  1  1  1  0 X+1  X  1  0 X+1 X+1  1  X  X  1  1  X X+1  0  0  0
 0  0  0  1  0  0  0  1  1  1  0 X+1 X+1  1  1 X+1  1  1  1  0  1  X X+1  0  X  X  1  0 X+1  X X+1  1  X  X  0 X+1  0  X  1  0
 0  0  0  0  1  0  1  1  0  1  0  1 X+1  X  X X+1  X  0 X+1  0  X  1  1  1 X+1  1 X+1  0  0  1  0 X+1  X  0  X  0 X+1 X+1  0 X+1
 0  0  0  0  0  1  1  0  1  1  X X+1 X+1  1  1  X  0  X X+1 X+1  0  1  X  0  1  0  1 X+1  1  1 X+1  X  0 X+1 X+1 X+1  0 X+1  1 X+1
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  0  X  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  X  0  X  0  X  X  X  X  0  0  X  X  0  0  0  0  X  0  0  X  X  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  X  X  X  0  X  0  X  X  0  X  0  0  0  0  X  0  X  0  0  0  X  0  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+83x^28+112x^29+324x^30+438x^31+685x^32+880x^33+1315x^34+1480x^35+1872x^36+2286x^37+2399x^38+2882x^39+2835x^40+3028x^41+2611x^42+2444x^43+2035x^44+1536x^45+1231x^46+822x^47+584x^48+316x^49+265x^50+124x^51+90x^52+34x^53+45x^54+2x^55+7x^56+1x^58+1x^62

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 90.3 seconds.