The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^52+126x^53+143x^54+192x^55+220x^56+250x^57+257x^58+260x^59+253x^60+240x^61+273x^62+232x^63+248x^64+244x^65+195x^66+166x^67+171x^68+166x^69+110x^70+94x^71+71x^72+50x^73+40x^74+14x^75+8x^76+12x^77+6x^78+2x^79

The gray image is a code over GF(2) with n=124, k=12 and d=52.
This code was found by Heurico 1.10 in 0.765 seconds.