The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1  1  1 12 10  1  1  1  1  1  1  1  0 12  1  6 10  6  6  6  1  1  4  2
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5 10 15  1  1 12  9  0  6  0  3  5  1  1 15  1  1  1  1  1  6  0 12  6
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  0  8  0  8  8  8  8  8  0  0  0  8  0  8  0  8  8
 0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  8  0  8  8  0  0  0  8  0  8  8  8  0  8  0  0  0  0  8  0  0  8
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  8  8  0  0  0  8  8  0  8  8  8  8  0  8  8  8  8  8  8  8  8  0  0  8  0  8
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  0  0  0  8  8  8  8  8  8  8  0  8  0  0  8  0  8  8  8  8  0  0  0  0  0  0  8
 0  0  0  0  0  0  8  0  8  0  0  8  8  0  0  8  8  0  8  0  0  0  8  8  8  8  8  8  8  0  0  0  0  8  8  0  0  0  8  0  8
 0  0  0  0  0  0  0  8  8  8  8  0  0  0  8  8  0  8  8  0  0  8  0  8  0  0  0  8  8  0  0  8  0  8  0  8  8  8  8  0  8

generates a code of length 41 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+92x^34+84x^35+304x^36+412x^37+1407x^38+1572x^39+3090x^40+2508x^41+3061x^42+1596x^43+1391x^44+404x^45+276x^46+76x^47+67x^48+4x^49+20x^50+8x^52+5x^54+2x^56+3x^58+1x^60

The gray image is a code over GF(2) with n=328, k=14 and d=136.
This code was found by Heurico 1.16 in 6.3 seconds.