The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  0  1  1  2  1  0  1  2  8  1  1  2  0  1  1  1  1  2  1  4  1
 0  2  0  6  0  6  8  6 12 14  6  2 14  0 14  8  2  6  6  2  2  6 14  2 14 12  0  4 12  6 12  0
 0  0 12  0  0  0  0  0  0  0  8  8  4  4  8  4  4  8  4  0  0 12 12  4 12  8  4  4  0  4 12  8
 0  0  0 12  0  0  0  0  0  0 12  8  8 12  0  4  8  4 12  8  4 12  0  4  4 12  8  0  4  8 12 12
 0  0  0  0 12  0  8  4  4  4  4  0  0  4  8  8  0  0  0 12 12  4  8  4  4  0 12  8  0  4  0  4
 0  0  0  0  0 12 12  4 12  8  8  0  8  4  4 12  4 12  0  0  4  4  8 12  8  4 12  4  8  8  8  8

generates a code of length 32 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+73x^24+156x^25+234x^26+562x^27+1021x^28+1918x^29+3674x^30+5558x^31+6345x^32+5570x^33+3778x^34+1942x^35+938x^36+514x^37+230x^38+122x^39+69x^40+34x^41+20x^42+8x^43+1x^44

The gray image is a code over GF(2) with n=256, k=15 and d=96.
This code was found by Heurico 1.16 in 8.15 seconds.