The generator matrix

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

generates a code of length 31 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+51x^26+88x^27+160x^28+704x^29+564x^30+976x^31+557x^32+704x^33+148x^34+88x^35+46x^36+2x^38+2x^40+1x^42+2x^44+2x^46

The gray image is a code over GF(2) with n=248, k=12 and d=104.
This code was found by Heurico 1.16 in 0.104 seconds.