The generator matrix

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

generates a code of length 81 over Z4 who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+24x^65+113x^66+216x^67+330x^68+446x^69+623x^70+740x^71+883x^72+996x^73+1160x^74+1326x^75+1510x^76+1650x^77+1584x^78+1758x^79+2009x^80+1940x^81+1839x^82+1856x^83+1811x^84+1710x^85+1520x^86+1448x^87+1199x^88+980x^89+786x^90+630x^91+550x^92+382x^93+240x^94+182x^95+119x^96+60x^97+58x^98+36x^99+30x^100+4x^101+9x^102+4x^104+4x^106+1x^112+1x^116

The gray image is a code over GF(2) with n=162, k=15 and d=65.
This code was found by Heurico 1.10 in 145 seconds.