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

generates a code of length 41 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+49x^32+96x^33+168x^34+278x^35+444x^36+436x^37+1634x^38+786x^39+3804x^40+950x^41+3951x^42+738x^43+1604x^44+466x^45+433x^46+222x^47+116x^48+90x^49+49x^50+24x^51+28x^52+10x^53+5x^54+2x^56

The gray image is a code over GF(2) with n=328, k=14 and d=128.
This code was found by Heurico 1.16 in 3.87 seconds.