The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  2  1  2  4  1  1  0  2  1  1  4  1  1  1  0  1  1  1  1  2  1  1  1
 0 12  0 12  0 12  0 12  0  4  8 12  0 12  4 12  0  0  8 12  0 12 12  0  8  4 12 12  4 12 12 12  8  4 12  0  4  4 12  0  0  0
 0  0  8  0  0  0  0  0  0  0  8  0  8  8  8  0  8  8  8  0  8  8  0  0  8  0  8  8  8  8  8  8  0  0  8  0  8  8  0  0  0  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  8  0  0  0  8  8  0  8  0  8  0  8  8  0  0  8  8  8  0  8  8  0  0  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  8  0  0  0  8  8  0  8  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  8  0  0  8  8  8  0  8  8  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  0  0  0  8  8  8  8  0  8  0  0  0  8  8  0  8  8  8  8  8  8  8  8  0
 0  0  0  0  0  0  0  8  0  8  0  8  0  8  0  8  8  8  8  0  0  0  8  0  8  0  0  8  8  8  0  8  0  8  0  0  8  0  0  8  8  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  8  8  8  0  8  8  0  0  0  8  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  0  0  0

generates a code of length 42 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+54x^32+51x^34+44x^35+121x^36+116x^37+163x^38+348x^39+1400x^40+516x^41+2593x^42+516x^43+1382x^44+348x^45+178x^46+116x^47+79x^48+44x^49+54x^50+33x^52+27x^54+2x^56+5x^58+1x^66

The gray image is a code over GF(2) with n=336, k=13 and d=128.
This code was found by Heurico 1.16 in 1.03 seconds.