The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+60x^78+184x^79+89x^80+96x^81+18x^82+32x^83+22x^84+4x^85+2x^86+4x^89

The gray image is a code over GF(2) with n=640, k=9 and d=312.
This code was found by Heurico 1.16 in 0.329 seconds.