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

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

Homogenous weight enumerator: w(x)=1x^0+141x^78+244x^80+106x^82+8x^84+9x^86+1x^88+2x^108

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 1.34 seconds.