The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+67x^34+137x^36+32x^37+317x^38+256x^39+801x^40+960x^41+765x^42+256x^43+267x^44+32x^45+101x^46+57x^48+28x^50+16x^52+2x^54+1x^64

The gray image is a code over GF(2) with n=328, k=12 and d=136.
This code was found by Heurico 1.16 in 0.289 seconds.