The generator matrix

 1  0  0  1  1  1 14  1  1  6  1  4  1  4  6  0  1  2  1  1  1  1  1  1  8  1  1  1  1  1 14  1  4  0 12  1 14  1
 0  1  0  2  1 11  1 12  2  0 15  1 13  1  1  2  2  1  6  0  5  1 13 13  1  6  6  8  1  9 12 12  1  1  1  3  1  0
 0  0  1  1  5  4  3  6  3  1  7  3  0  6  5  1  6  4 15  1 13 14  4 11  9 13  8 10  7  5  1  8  1  7 15  6  6  0
 0  0  0  4  4  8  4  8 12  0  4 12 12 12  8 12  4  8  0 12  0 12  0  0  4  0  4 12  4  8  4 12  0 12  8  8  4  0
 0  0  0  0  8  0  0  8  8  8  0  8  0  0  0  0  8  8  0  8  0  8  8  0  0  8  8  0  0  0  8  8  8  0  0  8  0  0

generates a code of length 38 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+106x^32+554x^33+1181x^34+2502x^35+3881x^36+5044x^37+6062x^38+5394x^39+3954x^40+2368x^41+1019x^42+444x^43+145x^44+62x^45+24x^46+10x^47+9x^48+2x^49+2x^50+2x^51+2x^53

The gray image is a code over GF(2) with n=304, k=15 and d=128.
This code was found by Heurico 1.16 in 5.15 seconds.