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

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

Homogenous weight enumerator: w(x)=1x^0+153x^32+16x^33+290x^34+92x^35+575x^36+636x^37+1562x^38+1592x^39+1633x^40+616x^41+442x^42+108x^43+278x^44+12x^45+118x^46+44x^48+20x^50+3x^52+1x^56

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 0.938 seconds.