The generator matrix

 1  1  1  1  1  1  1  1  2  0  1  1  2  1  1 12  1  1  2  0  1  1  1  1  2  2  2  2  1  1  1
 0  2 12  6  0  6 12 10  6  2  0  6 10 12 10  2  0  6  6  2 10 12  0  6  6  0  6  6  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  8  8  8  8  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  0  0  8  8  8  8  0  8  0  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  0  8  0  0  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  0  0  8  0  8  8  8  0  0  0  0  0  8  8
 0  0  0  0  0  0  8  0  0  0  0  8  0  8  8  0  0  8  8  8  0  8  0  0  0  8  8  0  0  8  8
 0  0  0  0  0  0  0  8  0  0  8  0  0  8  0  8  0  8  8  0  0  0  8  8  0  0  8  8  0  8  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  0  0  8  8  8  0  8  8  8  0  8  8  8  0  8  8  8
 0  0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  0  0  8  8  0  8  0  8  0  8  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+29x^20+63x^22+22x^23+179x^24+130x^25+553x^26+552x^27+2134x^28+2424x^29+8277x^30+3972x^31+8307x^32+2444x^33+2186x^34+552x^35+569x^36+120x^37+150x^38+22x^39+39x^40+2x^41+29x^42+4x^44+5x^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 5.53 seconds.