The generator matrix

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

generates a code of length 58 over Z4 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+52x^42+106x^43+219x^44+358x^45+619x^46+806x^47+1123x^48+1380x^49+1807x^50+2118x^51+2521x^52+2998x^53+3474x^54+3916x^55+4290x^56+4416x^57+4516x^58+4756x^59+4199x^60+4168x^61+3671x^62+3168x^63+2603x^64+2256x^65+1807x^66+1194x^67+1012x^68+682x^69+468x^70+264x^71+258x^72+108x^73+90x^74+50x^75+24x^76+18x^77+8x^78+6x^79+5x^80+1x^84

The gray image is a code over GF(2) with n=116, k=16 and d=42.
This code was found by Heurico 1.10 in 370 seconds.