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

generates a code of length 53 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+45x^52+15x^56+2x^68+1x^76

The gray image is a code over GF(2) with n=106, k=6 and d=52.
This code was found by Heurico 1.16 in 4.76 seconds.