The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+64x^35+398x^36+1284x^37+2100x^38+5120x^39+7170x^40+11160x^41+10885x^42+11328x^43+7209x^44+5102x^45+2068x^46+1088x^47+309x^48+174x^49+42x^50+16x^52+6x^53+8x^54+2x^57+1x^58+1x^60

The gray image is a code over GF(2) with n=336, k=16 and d=140.
This code was found by Heurico 1.16 in 22.1 seconds.