The generator matrix

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

generates a code of length 58 over Z4 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+20x^45+111x^46+206x^47+243x^48+404x^49+512x^50+536x^51+687x^52+856x^53+879x^54+948x^55+1066x^56+1078x^57+1158x^58+1146x^59+1075x^60+1036x^61+975x^62+854x^63+656x^64+536x^65+478x^66+332x^67+213x^68+152x^69+107x^70+72x^71+26x^72+14x^73+4x^74+2x^75+1x^92

The gray image is a code over GF(2) with n=116, k=14 and d=45.
This code was found by Heurico 1.10 in 11.7 seconds.