The generator matrix

 1  0  1  1  1 3X+2  1  1 3X+2  1  2  1  1  1  1 X+2  1  0 2X  1  1  1  0  1  1 3X  1  1 3X+2  1  1  2  1 3X  1  1  1  1  1  1 2X+2  X  1  2 3X  1  1  1  1  1  1 2X+2  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1 3X+2  1  1 3X  1  1  1
 0  1  1  2 X+1  1  X X+3  1  X  1 3X+3 X+1  3  0  1 3X+2  1  1 3X+3 2X+2 2X+1  1 3X 3X+3  1 3X+2 3X  1  3 2X  1 2X  1 X+1 3X+1 2X+1 2X+1 2X+3  3  1  1 3X  1  1 3X  2 2X+1 2X+2 2X+3 3X+2  0 3X+2 3X+2  2 3X+2 2X+2  2 3X+2 3X  0 2X  0 X+2 2X 2X+2  X  2  1 3X X+3  0 X+3 3X+1  2 X+2  1  2 3X+1  1 3X+1 3X+1  3
 0  0  X 3X 2X 3X 3X  X 2X+2  2 3X 2X+2 X+2 X+2 2X+2  0  0  2 3X 2X 3X+2 2X 3X+2 X+2 3X+2  0 2X+2  0 X+2 2X+2 X+2 X+2 3X  2  2  X X+2  2  X  0 2X  X 3X  2 X+2 3X+2  2 3X+2 2X  2  2  X 3X+2  X 2X+2 3X 2X+2  0 X+2 2X X+2 3X+2 3X  2  X  2  0 2X  2  2 2X 3X 3X+2 3X  X  0 3X+2 X+2 2X+2 3X  2  0 3X+2

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+367x^80+264x^81+444x^82+144x^83+282x^84+208x^85+208x^86+16x^87+60x^88+8x^89+28x^90+8x^92+8x^94+1x^108+1x^124

The gray image is a code over GF(2) with n=664, k=11 and d=320.
This code was found by Heurico 1.16 in 226 seconds.