The generator matrix

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

generates a code of length 37 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+72x^30+8x^31+124x^32+80x^33+144x^34+504x^35+697x^36+864x^37+680x^38+504x^39+156x^40+80x^41+96x^42+8x^43+38x^44+32x^46+5x^48+1x^52+2x^56

The gray image is a code over GF(2) with n=296, k=12 and d=120.
This code was found by Heurico 1.16 in 1.16 seconds.