The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+110x^38+8x^39+289x^40+96x^41+474x^42+672x^43+916x^44+656x^45+432x^46+88x^47+165x^48+16x^49+92x^50+59x^52+10x^54+9x^56+2x^58+1x^68

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 0.368 seconds.