The generator matrix

 1  0  1  1  1  4  1  1  2  1  1  6  8  1  1  1  8  1 10  1  1  1  0  1 14  1  1  1  6  4  1  1  1  1  0  2  1  2  1  1  1
 0  1  1  0  3  1  2  7  1  5  6  1  1  3 14  4  1 11  1  9 13  2  1 12  1  5  9 12  1  1 14  9 12 15  8  8  1  1  2 11  0
 0  0  2  6  0  2  2 14  6  4  4  0  0  4  8 10  6  6 14 10  0  6  2 10  8 14  8  4  0  4 14 14  6  0  2 10  2 10 12 12  0
 0  0  0 12  0  0  8  4  4  4 12  0 12 12  4  8 12  4  0  4  4 12 12  4 12  8  0 12  8  0  4  0  8  8  0 12  0 12  8  8  0
 0  0  0  0  8  0  0  0  0  8  0  0  0  8  0  0  8  0  8  8  0  8  8  8  8  8  8  8  8  0  8  0  8  0  0  0  8  8  0  8  0
 0  0  0  0  0  8  0  0  8  0  0  8  8  8  8  8  8  8  8  8  0  8  0  0  0  0  0  0  0  0  0  0  8  8  0  0  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+92x^34+244x^35+619x^36+1068x^37+2644x^38+3358x^39+5868x^40+5102x^41+5891x^42+3252x^43+2641x^44+1032x^45+537x^46+234x^47+106x^48+30x^49+17x^50+12x^51+12x^52+3x^54+4x^55+1x^56

The gray image is a code over GF(2) with n=328, k=15 and d=136.
This code was found by Heurico 1.16 in 7.17 seconds.