The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  4  2  2  8  2  1  0  8  2  2  0  2  1  1  1  1  1  2 12  2  1  1  1  1
 0  2  0  2  0  8  6 14  0  0  2 14  8  0  6 14 12  2 14  4  4  2  4 12  2  2 10  4  6 14  6  0  2 10  6  2 10 12  8  4  0
 0  0  2  2  0  6 14  8  0  2 14  0 10  4  0  6 12 14  4  2  2  4  8  2  2  4  2  2 10 12  2  8  0  8 10 10  2 10  6  4  8
 0  0  0  4  0  0 12  0 12 12  8  4 12 12 12  8  0  0  4  4  8  8  4 12  8 12  0  0  4  0 12  4 12 12  8  4 12 12  4  8  8
 0  0  0  0 12  4  4  4 12  8 12  0 12  0  4  8 12  4  4  4  0  8  0  8  0  8  4  4  4  0  4 12 12  4 12  8  4 12  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+50x^34+218x^35+441x^36+856x^37+1037x^38+1768x^39+2285x^40+3088x^41+2359x^42+1746x^43+1109x^44+770x^45+277x^46+196x^47+94x^48+52x^49+19x^50+8x^51+6x^52+2x^53+2x^54

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 2.87 seconds.