The generator matrix

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

generates a code of length 67 over Z4 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+54x^50+68x^51+227x^52+342x^53+580x^54+648x^55+932x^56+1148x^57+1601x^58+1866x^59+2135x^60+2620x^61+2960x^62+3320x^63+3617x^64+3996x^65+4082x^66+4422x^67+4221x^68+4182x^69+3850x^70+3622x^71+3138x^72+2722x^73+2278x^74+1792x^75+1440x^76+1056x^77+860x^78+532x^79+442x^80+256x^81+204x^82+106x^83+94x^84+56x^85+38x^86+6x^87+6x^88+6x^89+5x^90+2x^91+3x^92

The gray image is a code over GF(2) with n=134, k=16 and d=50.
This code was found by Heurico 1.10 in 229 seconds.