The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  1  1  1  1  1  1  2  X  2  X  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  2  1  1  1  2
 0  1 X+1 X+2  1  1 X+1  0  1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  1  1  0 X+1 X+2  3  0 X+1 X+2  3  1  1  1  1  1 X+3 X+3  1 X+3  3 X+3  1 X+3  3 X+3  1 X+3  3 X+3  1  2  X  2  X  2  X  2  X  2  X  2  X  2  0  X  2  X  0
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  0  2  0  0  2  0  2  2  2  2  2  0  0  0  0  2  2  0  2  2  2  0  0  2  0
 0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  2  2  0  0  0  2  2  2  2  2  0  0  0  2  2  0  2  0  2  0  0  0  2  2  2  0  0  2  0  2  2  0  2  2  0  0  0  0  2  2  2  0  2  0  0  0  0  2  2  0  2  0  2  0
 0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  0  0  2  0  2  0  0  0  0  2  2  2  2  0  2  2  0  0  2  2  0  2  0  2  2  0  0  0  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+188x^80+192x^82+96x^84+32x^88+2x^96+1x^128

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 94.8 seconds.