The generator matrix

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

generates a code of length 37 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+190x^28+508x^30+906x^32+1244x^34+768x^35+7361x^36+10752x^37+7406x^38+768x^39+1316x^40+902x^42+432x^44+174x^46+33x^48+6x^50+1x^68

The gray image is a code over GF(2) with n=296, k=15 and d=112.
This code was found by Heurico 1.16 in 12.5 seconds.