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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+187x^36+12x^37+340x^38+168x^39+720x^40+804x^41+1322x^42+1104x^43+1387x^44+820x^45+690x^46+136x^47+253x^48+28x^49+126x^50+65x^52+18x^54+10x^56+1x^60

The gray image is a code over GF(2) with n=344, k=13 and d=144.
This code was found by Heurico 1.16 in 53.2 seconds.