The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+46x^20+62x^21+93x^22+116x^23+72x^24+92x^25+105x^26+92x^27+56x^28+80x^29+79x^30+44x^31+47x^32+20x^33+11x^34+4x^35+2x^36+2x^37

The gray image is a linear code over GF(2) with n=52, k=10 and d=20.
This code was found by Heurico 1.10 in 0.031 seconds.