The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+62x^38+200x^39+440x^40+630x^41+1016x^42+1152x^43+1464x^44+1102x^45+885x^46+506x^47+301x^48+180x^49+136x^50+60x^51+32x^52+6x^53+12x^54+2x^55+2x^56+2x^57+1x^62

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 0.764 seconds.