The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+190x^56+144x^58+204x^60+122x^62+121x^64+52x^66+58x^68+44x^70+48x^72+20x^74+10x^76+2x^78+8x^80

The gray image is a code over GF(2) with n=124, k=10 and d=56.
This code was found by Heurico 1.16 in 0.972 seconds.