The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+107x^34+64x^35+440x^36+544x^37+1625x^38+2032x^39+4455x^40+3984x^41+6295x^42+4064x^43+4400x^44+2048x^45+1579x^46+496x^47+387x^48+80x^49+109x^50+40x^52+11x^54+5x^56+1x^58+1x^62

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 7.65 seconds.