The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+28x^80+144x^81+93x^82+70x^83+62x^84+40x^85+21x^86+18x^87+2x^88+12x^89+13x^90+4x^91+1x^96+1x^98+1x^100+1x^104

The gray image is a code over GF(2) with n=332, k=9 and d=160.
This code was found by Heurico 1.13 in 0.172 seconds.