The generator matrix

1 0 0 0 0 0 0 1 1 1 2 1 1 1 2 1 1 1 2 2 1 0 0 2 1 2 1 2 1 1 2 1 1 0 2 2 1 0 1 1 0 1 1 1 1 1 2 1 0 1 2 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 2 0 2 0 0 1 3 3 1 1 1 1 1 1 1 1 3 1 1 2 3 1 3 1 2 1 1 1
0 0 1 0 0 0 0 0 0 0 0 1 3 2 1 0 1 1 1 2 3 1 0 1 3 0 0 1 2 2 2 2 3 2 2 3 1 0 1 2 3 1 0 3 1 0 3 3 0 0 2 0 2
0 0 0 1 0 0 0 0 0 0 0 2 1 3 1 1 0 3 2 1 3 3 1 2 0 1 3 1 0 1 1 2 3 0 3 3 3 2 0 0 3 2 2 3 2 0 1 3 3 1 2 0 1
0 0 0 0 1 0 0 1 2 3 1 0 0 0 0 0 1 3 2 1 1 2 3 1 0 0 1 3 2 1 2 2 3 3 2 0 0 2 3 1 3 0 2 1 3 3 1 1 3 2 1 2 1
0 0 0 0 0 1 0 1 3 2 3 0 0 0 0 1 2 3 3 3 0 3 0 1 1 1 3 0 0 2 2 3 3 3 3 3 1 2 2 0 1 3 0 0 3 2 3 3 3 3 1 1 0
0 0 0 0 0 0 1 2 1 3 3 1 2 3 3 2 0 2 1 2 3 0 3 2 0 1 3 0 0 2 2 1 0 1 1 0 3 1 0 3 1 0 0 1 1 0 0 1 2 3 3 2 0

generates a code of length 53 over Z4 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+294x^42+790x^44+1104x^46+1578x^48+2050x^50+2345x^52+2372x^54+2068x^56+1718x^58+1108x^60+588x^62+280x^64+66x^66+21x^68+1x^96

The gray image is a code over GF(2) with n=106, k=14 and d=42.
This code was found by Heurico 1.10 in 13.4 seconds.