The generator matrix

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

generates a code of length 67 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+44x^52+106x^53+216x^54+340x^55+506x^56+648x^57+804x^58+908x^59+1136x^60+1336x^61+1508x^62+1714x^63+1836x^64+2000x^65+2013x^66+2188x^67+2114x^68+2092x^69+2034x^70+1820x^71+1626x^72+1354x^73+1128x^74+876x^75+725x^76+528x^77+388x^78+290x^79+189x^80+108x^81+86x^82+44x^83+12x^84+18x^85+14x^86+12x^87+2x^88+2x^89+1x^92+1x^98

The gray image is a code over GF(2) with n=134, k=15 and d=52.
This code was found by Heurico 1.10 in 107 seconds.