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

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

Homogenous weight enumerator: w(x)=1x^0+24x^82+5x^84+2x^86

The gray image is a code over GF(2) with n=640, k=5 and d=328.
This code was found by Heurico 1.16 in 0.328 seconds.