The generator matrix

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

generates a code of length 82 over Z4 who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+44x^65+136x^66+300x^67+435x^68+648x^69+858x^70+1116x^71+1383x^72+1638x^73+1978x^74+2222x^75+2554x^76+2924x^77+3143x^78+3430x^79+3825x^80+3886x^81+4001x^82+3958x^83+3719x^84+3718x^85+3430x^86+3082x^87+2812x^88+2288x^89+1948x^90+1654x^91+1235x^92+940x^93+704x^94+502x^95+333x^96+254x^97+158x^98+106x^99+70x^100+42x^101+24x^102+14x^103+13x^104+2x^105+2x^106+3x^108+1x^110+1x^112+1x^114

The gray image is a code over GF(2) with n=164, k=16 and d=65.
This code was found by Heurico 1.10 in 628 seconds.