The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  2  0  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  0  2  0  2  2  0  0
 0  0  2  0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  0  2  0  2  0  2  2  0  0  2  2  0  2  2  2  2  0  0  0  0  2  2  0  2  2  0  2  2  2  2  2  0  0  0  2  2  2  0  0  0
 0  0  0  2  0  0  0  0  0  0  2  0  2  0  2  2  2  0  0  0  2  2  2  2  0  0  2  0  2  2  2  0  0  2  2  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  2  0  2  2  2  0  0
 0  0  0  0  2  0  0  0  2  2  0  2  0  0  0  2  0  2  2  0  2  2  2  2  0  0  2  2  0  0  0  2  2  0  0  2  2  0  0  2  0  2  2  0  0  2  2  0  0  2  0  0  2  2  2  0  0  0
 0  0  0  0  0  2  0  2  2  2  0  0  0  0  0  0  2  2  0  2  2  0  2  2  0  2  2  0  0  2  0  0  2  2  2  0  0  2  2  0  2  0  2  0  2  0  0  2  2  2  0  0  2  2  0  0  0  0
 0  0  0  0  0  0  2  2  0  2  0  2  0  0  2  0  2  0  2  0  2  2  0  2  2  2  2  2  2  2  2  2  2  2  0  0  2  0  0  2  2  0  2  0  2  0  0  2  0  0  2  2  2  0  0  2  0  0

generates a code of length 58 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+19x^52+44x^56+128x^58+44x^60+19x^64+1x^116

The gray image is a code over GF(2) with n=116, k=8 and d=52.
This code was found by Heurico 1.16 in 0.041 seconds.