The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+32x^38+260x^39+338x^40+814x^41+830x^42+1308x^43+1260x^44+1278x^45+780x^46+588x^47+224x^48+266x^49+86x^50+84x^51+32x^52+10x^53+1x^64

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 0.701 seconds.