The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1  1 12  0  1  1  0  6  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  6  5  1 12 10 15  1  1  3  6  1  1  0  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  0  0  8  8  8  8  0  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  0  8  8  0  8  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  0  8  8  0  0  8  0  8  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  8  0  8  0  8  0  8  0  8  0  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  0  8  8  8  8  0  0  0  8  8  0  8  0  8  8  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  8  8  0  8  8  0  8  0  8  0  0  8  8  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  8  8  0  8  8  8  0  8  0  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+51x^20+55x^22+44x^23+166x^24+480x^25+297x^26+1616x^27+2723x^28+8736x^29+11035x^30+15112x^31+11047x^32+8736x^33+2728x^34+1616x^35+297x^36+480x^37+173x^38+44x^39+50x^40+46x^42+1x^44+1x^46+1x^58

The gray image is a code over GF(2) with n=248, k=16 and d=80.
This code was found by Heurico 1.16 in 12.6 seconds.