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

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+176x^78+80x^79+72x^80+32x^81+96x^82+16x^83+16x^84+16x^86+5x^88+1x^96+1x^104

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 0.547 seconds.