The generator matrix

 1  0  1  1  1 14  1  1  0  1  1  2  6  1  1  1 12  1  1  1  1  1  4  0  1 10  1  1 14  1  1  0  1  2  1  6  1  4  4  8  2  1  1  1
 0  1 11 14  5  1  0  3  1  6 13  1  1  4 15  1  1 10 12  7  9  8  1  1  2  1  4  5  1  6 13  1 10  1  3  1  0  2  8  2  8  7  3  0
 0  0 12  4  0  4 12  0 12  8 12  4  0  4  8  4  0  8  0  4  0 12  4  8  4  0 12  0  4  0  4  0  8 12  0  0  8  4  4  4  4 12  8  0
 0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  0  8  8  0  0  0  8  8  0  8  8  8  0  0  8  8  0  8  0  8  8  0  0  0  8  0  0  0  0
 0  0  0  0  8  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  8  8  0  8  8  0  0  8  8  8  8  0  0  0  8  8  8  0  0  0  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  0  8  0  0  8  8  8  0  8  8  0  0  8  0  8  0  8  0  0  0  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  0  8  8  0  8  8  8  0  8  8  0  0  0  8  8  8  8  0  8  0  8  0  8  8  8  8  8  8  0
 0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  0  0  0  8  0  0  8  0  8  0  8  8  0  8  0  0  0  8  0  8  0  0  0  8  8  8  0  0  0
 0  0  0  0  0  0  0  0  8  0  0  8  8  8  0  8  8  8  0  8  0  8  0  0  8  8  8  0  0  0  0  8  8  0  0  0  8  0  0  0  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+38x^34+38x^35+191x^36+236x^37+588x^38+914x^39+2981x^40+3870x^41+9114x^42+8264x^43+13101x^44+8236x^45+9117x^46+3888x^47+3015x^48+928x^49+535x^50+194x^51+145x^52+40x^53+54x^54+14x^55+19x^56+2x^57+8x^58+3x^60+1x^62+1x^66

The gray image is a code over GF(2) with n=352, k=16 and d=136.
This code was found by Heurico 1.16 in 28.8 seconds.