The generator matrix

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

generates a code of length 62 over Z4 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+19x^50+98x^51+170x^52+254x^53+302x^54+298x^55+347x^56+440x^57+497x^58+496x^59+493x^60+474x^61+510x^62+490x^63+449x^64+474x^65+484x^66+432x^67+354x^68+308x^69+234x^70+196x^71+145x^72+86x^73+63x^74+38x^75+23x^76+12x^77+2x^78+2x^80+1x^98

The gray image is a code over GF(2) with n=124, k=13 and d=50.
This code was found by Heurico 1.10 in 3.41 seconds.