The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+68x^36+122x^37+272x^38+392x^39+1216x^40+2330x^41+3816x^42+5382x^43+5668x^44+5326x^45+3844x^46+2310x^47+1165x^48+398x^49+228x^50+98x^51+60x^52+16x^53+28x^54+10x^55+10x^56+4x^58+4x^60

The gray image is a code over GF(2) with n=352, k=15 and d=144.
This code was found by Heurico 1.16 in 8.22 seconds.