The generator matrix

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

generates a code of length 25 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+79x^16+186x^17+346x^18+466x^19+731x^20+916x^21+1176x^22+1552x^23+1650x^24+1860x^25+1804x^26+1668x^27+1374x^28+984x^29+696x^30+384x^31+238x^32+146x^33+74x^34+26x^35+23x^36+4x^37

The gray image is a linear code over GF(2) with n=50, k=14 and d=16.
This code was found by Heurico 1.10 in 2.58 seconds.