The generator matrix

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

generates a code of length 68 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+113x^54+184x^55+384x^56+474x^57+623x^58+840x^59+1012x^60+1088x^61+1264x^62+1598x^63+1655x^64+1870x^65+1950x^66+2054x^67+2145x^68+2158x^69+2090x^70+1978x^71+1893x^72+1692x^73+1319x^74+1128x^75+933x^76+712x^77+568x^78+326x^79+238x^80+170x^81+112x^82+74x^83+52x^84+26x^85+21x^86+10x^87+5x^88+2x^89+4x^90+1x^92+1x^100

The gray image is a code over GF(2) with n=136, k=15 and d=54.
This code was found by Heurico 1.10 in 167 seconds.