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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+28x^42+16x^43+167x^44+16x^45+20x^46+5x^48+1x^52+2x^60

The gray image is a code over GF(2) with n=352, k=8 and d=168.
This code was found by Heurico 1.16 in 0.0459 seconds.