The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  2  1  1  1  2  2  2  1  1
 0 12  0  0  0  0  0  0  0  0  0 12  8  8  4  4  4 12 12  4 12  8 12  0  4  8  0  4  0 12  8 12  4  8  8  8 12  0
 0  0 12  0  0  0  0  0  0  0  4  0  4 12  4 12 12  8 12  8  4  4  0 12  8 12  4  4  8  0  8 12 12 12 12  8  0  0
 0  0  0 12  0  0  0  4 12 12  4 12  4  4 12  0  8  4  0  0 12  8  4  8  8  0  4  4  0  0  8  4  8  8  4  4  4  0
 0  0  0  0 12  0  4  4  4  0  8  8  0  4  4  4 12 12  0 12  8  4  8  8  0 12  0  0  0  8 12 12  8 12  0  4  8  0
 0  0  0  0  0 12  4  8  4  4  0  0  4 12  0  8 12  0 12  4  4  8 12  8  4  4  4  8  0  8 12  4 12  8  0  8  4  0
 0  0  0  0  0  0  8  8  0  8  8  8  0  8  8  0  8  0  0  8  0  0  8  8  0  8  8  8  8  8  0  0  0  8  0  0  8  0

generates a code of length 38 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+73x^28+74x^29+216x^30+264x^31+359x^32+440x^33+587x^34+958x^35+1509x^36+2326x^37+19107x^38+2386x^39+1493x^40+1018x^41+599x^42+422x^43+324x^44+216x^45+217x^46+62x^47+79x^48+22x^49+9x^50+4x^51+2x^52+1x^66

The gray image is a code over GF(2) with n=304, k=15 and d=112.
This code was found by Heurico 1.16 in 12.4 seconds.