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  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0
 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  2  2  2  0  0  2  2  0  2  2  2  2  2  2  0  2  2  2  2  0  0  0  0  0  0
 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  2  2  2  2  0  0  0  2  2  0  2  2  0  0  0  0  2  2  0  2  2  2  0  2  2  2  0  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  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  2  2
 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  2  2  0  0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  0  2  2  0  0  2  2  0  0  2

generates a code of length 62 over Z4 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+32x^62+31x^64

The gray image is a code over GF(2) with n=124, k=6 and d=62.
This code was found by Heurico 1.16 in 0.0517 seconds.