The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  8  2  1  0  8  1  1  2  1  1  2  0  1  1 12  1  1  1 12  1  4  1  1
 0  2  0  6  0 14 10  8  6  8  2  8  0  8  6  2  2 14 10  2  2  4 12 14  4 10  6  2 12 10  2 12  0 14  2  4  8 14  0
 0  0 12  0  0  0  0  4  4  8  4  4  8 12  0  8 12  4 12  4  8  0  8  0  4  4  8  4  4  0 12  8  4 12  0  4  4  4  0
 0  0  0 12  0  8 12  0 12  4 12 12  4 12 12  4 12  8  0  8  0  8  0  0  8 12  8  0  4  8  4  4  8  0  8  8  4  0  0
 0  0  0  0 12 12  4 12  8  0 12  4 12  8  4  0  4  0 12 12 12  4  8 12  8  8  8  8  8  4  0  4  0  8  8  4 12  8  0

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

Homogenous weight enumerator: w(x)=1x^0+43x^32+76x^33+191x^34+370x^35+588x^36+924x^37+1241x^38+1386x^39+1226x^40+948x^41+603x^42+272x^43+128x^44+94x^45+37x^46+18x^47+30x^48+4x^49+6x^50+2x^51+2x^53+2x^54

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 0.718 seconds.