The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+100x^32+38x^34+322x^36+32x^37+260x^38+192x^39+960x^40+1504x^41+3372x^42+2688x^43+3609x^44+1504x^45+776x^46+192x^47+446x^48+32x^49+158x^50+145x^52+4x^54+44x^56+3x^60+1x^64+1x^68

The gray image is a code over GF(2) with n=344, k=14 and d=128.
This code was found by Heurico 1.16 in 4.19 seconds.