The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+244x^31+1236x^32+3860x^33+9139x^34+17486x^35+30361x^36+43590x^37+49648x^38+43806x^39+31442x^40+17828x^41+8473x^42+3282x^43+1177x^44+422x^45+94x^46+30x^47+7x^48+12x^49+6x^50

The gray image is a code over GF(2) with n=304, k=18 and d=124.
This code was found by Heurico 1.16 in 318 seconds.