The generator matrix

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

generates a code of length 69 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+40x^54+118x^55+261x^56+384x^57+563x^58+642x^59+763x^60+954x^61+1077x^62+1266x^63+1470x^64+1690x^65+1863x^66+2068x^67+2082x^68+2130x^69+2128x^70+2020x^71+1934x^72+1770x^73+1608x^74+1366x^75+1143x^76+946x^77+677x^78+558x^79+431x^80+258x^81+219x^82+132x^83+84x^84+50x^85+14x^86+22x^87+15x^88+10x^89+3x^90+8x^92

The gray image is a code over GF(2) with n=138, k=15 and d=54.
This code was found by Heurico 1.10 in 55.3 seconds.