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

generates a code of length 80 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+88x^77+122x^78+236x^79+150x^80+232x^81+94x^82+80x^83+8x^84+6x^86+4x^87+2x^90+1x^128

The gray image is a code over GF(2) with n=640, k=10 and d=308.
This code was found by Heurico 1.16 in 0.812 seconds.