The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  8  1  2  1  0  1  1  2  1  4  2  1  1  1  2  1  1  4  1  1  2  1  1  1  1  2  2  1
 0  2  0  6  4 14 12  2  0  6 12 10  8  2  2 14 14 14  2  0  4  2  4  2  6  4  2  8  6  0  0  0 10  4 14 14 12 14 14 14  2  0
 0  0 12  0  4  4  8  4  0  8  0  8  4  4 12 12  4  0  8  0 12 12  4  4  8  0  4  4  0  8  4 12  0 12  4 12  8  8  8 12  4  0
 0  0  0  8  0  0  8  0  0  8  0  0  8  0  0  0  8  8  8  8  0  8  8  0  0  8  8  8  0  8  8  0  8  8  0  8  0  0  0  0  0  0
 0  0  0  0  8  0  0  8  8  8  0  8  0  0  0  8  8  8  0  8  0  0  8  8  0  0  8  8  8  8  0  0  8  0  0  0  8  8  8  8  0  0
 0  0  0  0  0  8  0  8  0  0  8  8  8  0  0  0  8  8  8  8  8  0  0  8  0  8  8  0  8  0  0  8  8  8  0  0  0  8  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+49x^36+86x^37+171x^38+290x^39+589x^40+552x^41+738x^42+514x^43+532x^44+240x^45+155x^46+86x^47+42x^48+16x^49+18x^50+6x^51+2x^52+2x^53+5x^54+1x^60+1x^62

The gray image is a code over GF(2) with n=336, k=12 and d=144.
This code was found by Heurico 1.16 in 0.261 seconds.