The generator matrix

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

generates a code of length 31 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+33x^20+58x^22+26x^23+151x^24+96x^25+333x^26+266x^27+930x^28+2464x^29+1543x^30+4548x^31+1553x^32+2464x^33+978x^34+244x^35+373x^36+96x^37+120x^38+34x^39+23x^40+33x^42+2x^43+8x^44+7x^46

The gray image is a code over GF(2) with n=248, k=14 and d=80.
This code was found by Heurico 1.16 in 2.04 seconds.