The generator matrix

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

generates a code of length 24 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+72x^16+158x^17+267x^18+392x^19+487x^20+610x^21+743x^22+836x^23+926x^24+916x^25+808x^26+708x^27+488x^28+348x^29+208x^30+108x^31+73x^32+14x^33+21x^34+4x^35+1x^36+2x^37+1x^38

The gray image is a linear code over GF(2) with n=48, k=13 and d=16.
This code was found by Heurico 1.10 in 0.672 seconds.