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

generates a code of length 62 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+120x^56+120x^60+213x^64+8x^68+48x^72+1x^80+1x^112

The gray image is a code over GF(2) with n=124, k=9 and d=56.
This code was found by Heurico 1.16 in 0.226 seconds.