The generator matrix

 1  0  0  0  1  1  1  2  1  1  2  1  1  0  0  1  1  1  2  1  1  0  0  2  1  2  2  1  1  0  1  1  2  2  0  1  1  1  2  1  0  1  0  0  1  1  2  0  0  2  1  1  1  1  2  0  2  1  0  1  1  2
 0  1  0  0  0  0  0  0  1  1  1  1  3  1  1  2  0  2  2  3  1  1  1  0  3  1  2  0  3  1  2  3  1  1  1  0  3  2  1  3  1  0  0  1  0  0  1  2  2  2  2  2  3  0  1  1  1  3  2  3  0  0
 0  0  1  0  0  1  3  1  3  1  0  0  2  1  3  2  0  1  0  3  2  3  2  1  3  3  1  1  0  0  0  2  2  2  0  3  1  2  1  1  1  1  2  0  1  1  3  2  1  2  3  3  3  2  3  3  3  2  2  3  2  1
 0  0  0  1  1  1  0  1  2  3  1  1  2  3  2  1  2  2  1  0  2  3  2  0  1  0  3  1  2  3  0  1  1  0  0  1  0  3  1  0  1  3  1  2  2  1  2  1  1  1  1  3  1  2  3  1  0  3  1  1  1  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  0  0  2  0  2  0  2  0  2  2  0  0  2  2  0  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  2  0  2  0
 0  0  0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  2  0  0  2  2  2  2  0  2  2  0  2  2  0  0  2  0  0  2  2  2  0  0  2  2  2  0  0  2  0  0  0  2  2  0  0  2  0  2  0  2  2  2  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+128x^58+249x^60+48x^62+169x^64+44x^66+86x^68+28x^70+46x^72+4x^74+25x^76+4x^78+2x^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 28.1 seconds.