The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+56x^77+98x^78+92x^79+87x^80+76x^81+34x^82+12x^83+24x^84+8x^85+9x^86+8x^87+4x^93+1x^94+1x^98+1x^106

The gray image is a code over GF(2) with n=320, k=9 and d=154.
This code was found by Heurico 1.13 in 0.156 seconds.