The generator matrix

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

generates a code of length 67 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+84x^54+130x^55+283x^56+354x^57+444x^58+562x^59+607x^60+688x^61+853x^62+846x^63+844x^64+968x^65+945x^66+1052x^67+1029x^68+984x^69+913x^70+934x^71+806x^72+736x^73+621x^74+494x^75+386x^76+258x^77+202x^78+130x^79+126x^80+38x^81+33x^82+12x^83+14x^84+6x^85+1x^114

The gray image is a code over GF(2) with n=134, k=14 and d=54.
This code was found by Heurico 1.10 in 14.4 seconds.