The generator matrix

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

generates a code of length 58 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+22x^54+46x^55+41x^56+36x^57+25x^58+24x^59+13x^60+8x^61+7x^62+2x^63+8x^64+4x^65+4x^66+4x^67+5x^70+4x^71+1x^74+1x^76

The gray image is a code over GF(2) with n=116, k=8 and d=54.
This code was found by Heurico 1.10 in 0.015 seconds.