The generator matrix

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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+14x^41+102x^42+6x^44+1x^48+2x^49+2x^54

The gray image is a code over GF(2) with n=336, k=7 and d=164.
This code was found by Heurico 1.16 in 0.0666 seconds.