The generator matrix

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

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+54x^15+117x^16+100x^17+76x^18+98x^19+152x^20+120x^21+40x^22+90x^23+106x^24+36x^25+12x^26+14x^27+8x^28

The gray image is a linear code over GF(2) with n=40, k=10 and d=15.
This code was found by Heurico 1.16 in 0.138 seconds.