The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+98x^32+146x^33+469x^34+594x^35+1275x^36+1606x^37+2726x^38+2516x^39+2851x^40+1622x^41+1299x^42+500x^43+359x^44+138x^45+101x^46+36x^47+22x^48+8x^49+12x^50+2x^51+2x^52+1x^54

The gray image is a code over GF(2) with n=312, k=14 and d=128.
This code was found by Heurico 1.16 in 2.6 seconds.