The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+154x^38+108x^39+512x^40+536x^41+1006x^42+1152x^43+1369x^44+1136x^45+968x^46+556x^47+389x^48+88x^49+128x^50+8x^51+46x^52+14x^54+18x^56+2x^58+1x^60

The gray image is a code over GF(2) with n=352, k=13 and d=152.
This code was found by Heurico 1.16 in 3.5 seconds.