The generator matrix

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

generates a code of length 62 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+174x^54+177x^56+430x^58+80x^60+452x^62+144x^64+244x^66+48x^68+174x^70+51x^72+62x^74+11x^80

The gray image is a code over GF(2) with n=124, k=11 and d=54.
This code was found by Heurico 1.16 in 66.9 seconds.