The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+81x^32+32x^33+213x^34+128x^35+607x^36+736x^37+1690x^38+1280x^39+1637x^40+736x^41+602x^42+128x^43+211x^44+32x^45+44x^46+16x^48+9x^50+5x^52+2x^54+1x^56+1x^60

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 0.794 seconds.