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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+138x^34+4x^35+461x^36+124x^37+866x^38+296x^39+1904x^40+1736x^41+4035x^42+3952x^43+5551x^44+3968x^45+4217x^46+1816x^47+1925x^48+312x^49+856x^50+76x^51+353x^52+4x^53+116x^54+42x^56+11x^58+2x^60+1x^62+1x^76

The gray image is a code over GF(2) with n=352, k=15 and d=136.
This code was found by Heurico 1.16 in 18.5 seconds.