The generator matrix

 1  0  1  1  1 12  1 14  1  2  1  1  1  1  1  8  1  1  4  2  1  6  1  1  1  1  1  1  2  2  1 12 12  1  4  1  1  0  1
 0  1  1  0  3  1  7  1 14  1 10  5  3 13  2  1 15 10  1  1  4  1  4  7  4 13  0 13 12 12 14  1  2 12  2 15  6  0  0
 0  0  2  6  0  2  6  8  0  2  6  4 12  4 14  8  2  0  6 12  0 14  2  2  4 12  2 10 10  6 10 12 14  6  2  0  0  8  0
 0  0  0 12  0 12  4  4  4  8  0  4  4  8 12  4 12  0 12  0 12  8  0  8 12  0  4  0  4  4  8  8  8 12 12  4  0  4  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  8  8  0  8  8  8  8  0  8  0  0  8  8  8  8  8  8  0  8  0  8  0  8  0
 0  0  0  0  0  8  0  0  0  8  0  0  0  0  8  0  0  8  8  0  8  0  8  8  8  8  8  0  0  8  0  8  8  8  0  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+69x^32+254x^33+714x^34+1138x^35+2665x^36+3238x^37+5961x^38+4964x^39+5539x^40+3484x^41+2623x^42+1044x^43+727x^44+176x^45+103x^46+20x^47+23x^48+14x^49+7x^50+2x^51+2x^53

The gray image is a code over GF(2) with n=312, k=15 and d=128.
This code was found by Heurico 1.16 in 6.73 seconds.