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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+174x^32+16x^33+272x^34+248x^35+812x^36+696x^37+1360x^38+1104x^39+1318x^40+800x^41+696x^42+184x^43+308x^44+24x^45+96x^46+67x^48+8x^50+8x^52

The gray image is a code over GF(2) with n=312, k=13 and d=128.
This code was found by Heurico 1.16 in 0.977 seconds.