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

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+45x^80+12x^81+65x^82+26x^83+40x^84+20x^85+28x^86+4x^87+10x^88+3x^98+2x^99

The gray image is a code over GF(2) with n=332, k=8 and d=160.
This code was found by Heurico 1.16 in 0.396 seconds.