The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1
0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 0 2X 0 2X 0 2X 0 2X 2 0 2X 2 0 2X 2 2 0 2X 2 2 2 2 0 2X 2X+2 2 0 2X 2X+2 2 0 0 2X 2X 2X+2 2X+2 2X+2 2 0 2X+2 2X+2 0 0
0 0 2X 0 0 0 2X 0 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 2X 0 0 0 2X 2X 2X 0 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0
0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 0 0 0 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 2X 2X 2X 0 0 2X 0 2X 2X 0 0 2X 0 2X 0
0 0 0 0 2X 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 2X 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 0 2X 2X 2X 0 2X 0 0 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 0 0 2X 0 2X 0 2X 0
generates a code of length 83 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 80.
Homogenous weight enumerator: w(x)=1x^0+17x^80+28x^81+22x^82+398x^83+12x^84+16x^85+3x^86+2x^88+4x^89+6x^90+1x^102+2x^115
The gray image is a code over GF(2) with n=664, k=9 and d=320.
This code was found by Heurico 1.16 in 0.609 seconds.