The generator matrix

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

generates a code of length 62 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+124x^52+286x^54+429x^56+482x^58+577x^60+478x^62+488x^64+410x^66+358x^68+216x^70+165x^72+44x^74+27x^76+4x^78+5x^80+2x^84

The gray image is a code over GF(2) with n=124, k=12 and d=52.
This code was found by Heurico 1.16 in 2.24 seconds.