The generator matrix

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

generates a code of length 78 over Z4 who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+44x^63+155x^64+286x^65+450x^66+618x^67+795x^68+896x^69+1000x^70+1148x^71+1293x^72+1464x^73+1575x^74+1680x^75+1873x^76+1934x^77+1969x^78+2036x^79+1881x^80+1860x^81+1821x^82+1568x^83+1357x^84+1186x^85+994x^86+854x^87+635x^88+446x^89+309x^90+202x^91+179x^92+104x^93+60x^94+38x^95+19x^96+16x^97+13x^98+4x^99+4x^100+1x^126

The gray image is a code over GF(2) with n=156, k=15 and d=63.
This code was found by Heurico 1.10 in 133 seconds.