The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+178x^38+64x^39+484x^40+544x^41+886x^42+1440x^43+1089x^44+1440x^45+834x^46+544x^47+434x^48+64x^49+118x^50+30x^52+28x^54+8x^56+4x^58+1x^60+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 1.52 seconds.