The generator matrix

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

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+7x^16+16x^17+17x^18+16x^19+20x^20+16x^21+10x^22+16x^23+4x^24+2x^26+2x^30+1x^34

The gray image is a linear code over GF(2) with n=40, k=7 and d=16.
This code was found by Heurico 1.16 in 0.00141 seconds.