The generator matrix

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

generates a code of length 24 over Z2[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+70x^15+152x^16+286x^17+502x^18+650x^19+936x^20+1290x^21+1496x^22+1768x^23+1925x^24+1842x^25+1663x^26+1284x^27+937x^28+678x^29+403x^30+250x^31+142x^32+64x^33+31x^34+10x^35+3x^36+1x^38

The gray image is a linear code over GF(2) with n=48, k=14 and d=15.
This code was found by Heurico 1.10 in 2.38 seconds.