The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1 12  1  1 10  1  0  1  1  1  1  6  1  1  1  1 10  1  1  1  6 12  1  6  1  2  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5  1 12 15  1 10  1  9  6  5  0  1 12  0  3 15  1  3 10 12  1  1  3  1  5  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  8  0  0  0  0  0
 0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  8  8  8  8  0  0  0  8  8  0  8  8  0  8  0  0  8  0  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  0  8  0  0  0  0  0  8  8  8  8  8  0  0  8  8  0  0  8  8  8  0  0  0
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  0  8  8  8  0  8  8  8  0  0  0  8  0  8  0  8  0  0  0  0  8  8  0  8  8  0  0  0  0
 0  0  0  0  0  0  8  0  8  0  0  8  8  0  0  8  8  0  8  8  0  0  0  0  8  0  8  0  8  8  8  0  0  8  8  0  8  8  0  0  8  0  8  0
 0  0  0  0  0  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  8  0  8  0  8  8  8  0  8  8  8  0  8  0  0  0  0  8  8  0  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+41x^36+34x^37+179x^38+184x^39+536x^40+1416x^41+1375x^42+3496x^43+1924x^44+3468x^45+1343x^46+1416x^47+527x^48+200x^49+162x^50+24x^51+33x^52+2x^53+5x^54+6x^56+7x^58+2x^60+1x^62+2x^64

The gray image is a code over GF(2) with n=352, k=14 and d=144.
This code was found by Heurico 1.16 in 2.08 seconds.