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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  0  0  2  0  2  0  2  0  2  0  2  2  2  0  0  2
 0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  0  2  2  0  2  2  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  0  0  2  0
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  0  0  2  2  0  0  0  2  2  2  2  2  0  2  0  0  0  0
 0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  0  2  2  0  2  2  0  0  0  2  2  0  0  0  0  0  2  0  2  2  2  0  0  2  2  0
 0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  2  0  0  2  2  2  2  2  0  0  0  0  2  2  0  0  0  0  2  2  2  0  0  2  2  2  0  0  0  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+59x^80+158x^82+23x^84+12x^88+1x^100+2x^114

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 0.288 seconds.