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

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+73x^80+32x^81+68x^82+32x^83+20x^84+12x^86+12x^88+4x^92+2x^96

The gray image is a code over GF(2) with n=328, k=8 and d=160.
This code was found by Heurico 1.16 in 0.284 seconds.