The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+71x^52+94x^53+141x^54+200x^55+230x^56+274x^57+227x^58+250x^59+292x^60+240x^61+234x^62+240x^63+235x^64+234x^65+181x^66+234x^67+163x^68+132x^69+143x^70+78x^71+78x^72+44x^73+31x^74+20x^75+18x^76+6x^77+2x^78+2x^79+1x^82

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 2.29 seconds.