The generator matrix

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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+184x^35+491x^36+900x^37+1412x^38+2182x^39+3709x^40+5116x^41+5194x^42+4536x^43+3742x^44+2480x^45+1330x^46+752x^47+423x^48+204x^49+62x^50+24x^51+15x^52+4x^53+2x^54+2x^55+3x^56

The gray image is a code over GF(2) with n=336, k=15 and d=140.
This code was found by Heurico 1.16 in 10.3 seconds.