The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+42x^31+56x^32+60x^33+98x^34+136x^35+188x^36+1308x^37+336x^38+1276x^39+240x^40+148x^41+68x^42+72x^43+4x^44+20x^45+10x^47+22x^48+10x^50+1x^64

The gray image is a code over GF(2) with n=304, k=12 and d=124.
This code was found by Heurico 1.16 in 60.9 seconds.