The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+232x^80+64x^82+208x^84+5x^96+2x^112

The gray image is a code over GF(2) with n=328, k=9 and d=160.
This code was found by Heurico 1.16 in 28.8 seconds.