The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  8  0  1  1  4  2  1  1  4  4  2  1  1  1  1  1  4  1  1  2  1  0  1
 0  2  0  2  0  0  2 10  8  2  4  6  6 14  4  4  6  0 10  0  2  8  2  2 10 10  4  4  8  2  2  0 12 14  2  2 14  8  2 10  2 12
 0  0  2  2  0  6 10  8  6 14  0  0  6 12  6  8 12  6  2  2  0  2 14 10  8  4 14  2  2 12 10  0  4 14  0  6  6  4  6  8  0  2
 0  0  0  4  0  0  4  0  0  4  8  8 12  8  0  0  0 12  8 12  8  8  8 12  4 12  4  8  8 12  4 12 12  0  4  4  8 12 12  4 12  4
 0  0  0  0 12  0 12  4  4  8  4  0 12 12  4  8  4 12 12  8  0  4 12  4 12  8  8  8 12 12  4  4  4 12 12 12  8 12  4  8  4  0
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  8  8  0  8  0  0  0  8  0  0  0  0  8  8  8  8  0  8  8  8  0  0  0  8  8  0  0

generates a code of length 42 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+54x^34+192x^35+455x^36+812x^37+1228x^38+2282x^39+3690x^40+4898x^41+5601x^42+4950x^43+3606x^44+2338x^45+1276x^46+666x^47+349x^48+198x^49+88x^50+34x^51+27x^52+10x^53+8x^54+4x^55+1x^58

The gray image is a code over GF(2) with n=336, k=15 and d=136.
This code was found by Heurico 1.16 in 11 seconds.