The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+153x^38+16x^39+175x^40+80x^41+436x^42+672x^43+1092x^44+672x^45+394x^46+80x^47+153x^48+16x^49+92x^50+44x^52+13x^54+6x^56+1x^72

The gray image is a code over GF(2) with n=352, k=12 and d=152.
This code was found by Heurico 1.16 in 2.77 seconds.