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  1  1  1  1  2  1  1  1  1  1  2  2  1  1  1  1  2  1  1
 0  8  0  0  0  0  0  0  0  8  8  8  0  8  0  0  8  0  8  8  0  0  0  0  0  8  0  0  8  8  0  8  0  8  8  8  8  8  0  8  8  8
 0  0  8  0  0  0  0  0  8  8  8  8  0  0  0  8  0  8  8  0  0  0  0  0  0  0  8  8  8  0  8  8  8  0  8  8  0  0  8  0  8  0
 0  0  0  8  0  0  0  0  8  0  0  8  0  8  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  0  8  0  8  8  0  8  8  8  8  0  8  0
 0  0  0  0  8  0  0  0  8  0  8  8  8  0  0  8  8  0  0  8  8  8  8  8  0  0  0  0  0  0  8  8  0  8  8  8  0  0  8  8  8  0
 0  0  0  0  0  8  0  0  8  0  8  0  0  8  8  8  0  0  8  8  0  0  0  8  8  8  8  0  8  8  8  0  8  0  0  8  8  0  0  0  8  8
 0  0  0  0  0  0  8  0  8  8  0  0  0  8  8  0  8  8  8  0  0  0  8  8  0  0  0  0  8  0  8  0  8  8  8  0  8  0  8  8  8  8
 0  0  0  0  0  0  0  8  8  8  0  8  8  0  8  0  0  0  8  8  0  8  8  0  0  0  0  8  8  8  0  0  8  0  8  8  8  8  8  8  0  0

generates a code of length 42 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+80x^36+166x^40+1632x^42+59x^44+32x^46+49x^48+28x^52+1x^76

The gray image is a code over GF(2) with n=336, k=11 and d=144.
This code was found by Heurico 1.16 in 17.3 seconds.