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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+52x^42+100x^43+147x^44+210x^45+251x^46+500x^47+752x^48+1246x^49+1718x^50+1244x^51+760x^52+514x^53+220x^54+172x^55+112x^56+74x^57+54x^58+32x^59+13x^60+4x^61+9x^62+6x^64+1x^80

The gray image is a code over GF(2) with n=400, k=13 and d=168.
This code was found by Heurico 1.16 in 1.3 seconds.