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

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

Homogenous weight enumerator: w(x)=1x^0+170x^38+146x^40+562x^42+512x^43+1373x^44+512x^45+531x^46+107x^48+126x^50+34x^52+18x^54+2x^56+1x^62+1x^76

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 29.4 seconds.