The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+106x^31+434x^32+848x^33+1454x^34+2070x^35+3994x^36+4622x^37+5669x^38+4650x^39+4033x^40+2280x^41+1378x^42+618x^43+360x^44+134x^45+73x^46+28x^47+10x^48+4x^49+2x^50

The gray image is a code over GF(2) with n=304, k=15 and d=124.
This code was found by Heurico 1.16 in 9.21 seconds.