The generator matrix

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

generates a code of length 58 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+72x^44+88x^45+312x^46+360x^47+621x^48+692x^49+894x^50+1120x^51+1326x^52+1530x^53+1688x^54+2062x^55+1998x^56+2214x^57+2304x^58+2446x^59+2222x^60+2122x^61+1837x^62+1692x^63+1380x^64+996x^65+874x^66+624x^67+454x^68+258x^69+246x^70+122x^71+104x^72+34x^73+32x^74+18x^75+14x^76+2x^77+5x^78+4x^79

The gray image is a code over GF(2) with n=116, k=15 and d=44.
This code was found by Heurico 1.10 in 47.4 seconds.