The generator matrix

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

generates a code of length 31 over Z16 who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+58x^23+141x^24+166x^25+242x^26+424x^27+462x^28+796x^29+3249x^30+5244x^31+3252x^32+908x^33+500x^34+380x^35+210x^36+172x^37+94x^38+34x^39+29x^40+6x^41+10x^42+4x^43+1x^46+1x^48

The gray image is a code over GF(2) with n=248, k=14 and d=92.
This code was found by Heurico 1.16 in 2.48 seconds.