The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  2  1  1  1  2  2
 0 12  0  0  0  0  0  0  0  0  0 12  8  8 12  4  4 12  4 12  4  4  4 12  8  0  4 12 12 12 12 12
 0  0 12  0  0  0  0  0  0  0  4  0  4 12 12  8  4  4  8  4  0  8  4  8 12  4  0  4 12 12  4  4
 0  0  0 12  0  0  0  4 12 12  4 12  4  4  0  4 12  8 12  0  8  8  0  0 12  8  8  4 12  8  8  4
 0  0  0  0 12  0  4  4  4  0  8  8  0  4  8  4  4  8 12 12  4  8 12  4  8 12  8 12  0  8  8  0
 0  0  0  0  0 12  4  8  4  4  0  0  4 12  4  4  4  8  8  8  4  4  8  0  0  0 12 12  0 12 12  0
 0  0  0  0  0  0  8  8  0  8  8  8  0  8  0  8  0  8  0  0  8  0  8  0  0  0  8  8  8  8  8  8

generates a code of length 32 over Z16 who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+70x^23+155x^24+202x^25+330x^26+428x^27+496x^28+886x^29+1553x^30+2504x^31+19456x^32+2520x^33+1627x^34+892x^35+529x^36+424x^37+289x^38+194x^39+95x^40+62x^41+39x^42+8x^43+3x^44+2x^45+2x^46+1x^56

The gray image is a code over GF(2) with n=256, k=15 and d=92.
This code was found by Heurico 1.16 in 9.6 seconds.