The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^20+8x^21+129x^22+66x^23+227x^24+244x^25+448x^26+754x^27+2159x^28+2792x^29+5180x^30+8604x^31+5187x^32+2880x^33+2168x^34+748x^35+464x^36+208x^37+222x^38+66x^39+103x^40+12x^41+40x^42+2x^43+7x^44+4x^46+2x^48+1x^54

The gray image is a code over GF(2) with n=248, k=15 and d=80.
This code was found by Heurico 1.16 in 7.25 seconds.