The generator matrix

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

generates a code of length 37 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+58x^31+111x^32+126x^33+189x^34+400x^35+760x^36+912x^37+693x^38+388x^39+186x^40+94x^41+66x^42+42x^43+28x^44+20x^45+11x^46+6x^47+2x^48+2x^51+1x^58

The gray image is a code over GF(2) with n=296, k=12 and d=124.
This code was found by Heurico 1.16 in 0.331 seconds.