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

generates a code of length 42 over Z4 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+345x^32+756x^34+1311x^36+1892x^38+2475x^40+2688x^42+2651x^44+1996x^46+1252x^48+664x^50+253x^52+64x^54+31x^56+4x^58+1x^60

The gray image is a code over GF(2) with n=84, k=14 and d=32.
This code was found by Heurico 1.10 in 23.9 seconds.