The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+123x^34+140x^35+480x^36+692x^37+1383x^38+2624x^39+2688x^40+5776x^41+5028x^42+5736x^43+2745x^44+2632x^45+1258x^46+704x^47+457x^48+112x^49+127x^50+12x^51+22x^52+4x^53+15x^54+6x^56+2x^58+1x^60

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 10.7 seconds.