The generator matrix

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

generates a code of length 70 over Z4 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+38x^55+124x^56+278x^57+383x^58+482x^59+644x^60+844x^61+1027x^62+1130x^63+1322x^64+1484x^65+1662x^66+1828x^67+1912x^68+2072x^69+2043x^70+2100x^71+2058x^72+1832x^73+1832x^74+1620x^75+1385x^76+1190x^77+889x^78+762x^79+607x^80+404x^81+312x^82+180x^83+127x^84+68x^85+33x^86+50x^87+8x^88+18x^89+10x^90+2x^91+3x^92+2x^93+1x^100+1x^106

The gray image is a code over GF(2) with n=140, k=15 and d=55.
This code was found by Heurico 1.10 in 115 seconds.