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

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

Homogenous weight enumerator: w(x)=1x^0+40x^36+88x^37+122x^38+188x^39+266x^40+254x^41+1129x^42+588x^43+3061x^44+374x^45+1149x^46+300x^47+214x^48+138x^49+72x^50+68x^51+55x^52+42x^53+21x^54+8x^55+11x^56+2x^58+1x^66

The gray image is a code over GF(2) with n=352, k=13 and d=144.
This code was found by Heurico 1.16 in 1.08 seconds.