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

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+13x^76+44x^77+53x^78+90x^79+127x^80+80x^81+47x^82+36x^83+9x^84+4x^85+3x^86+2x^87+2x^88+1x^154

The gray image is a code over GF(2) with n=320, k=9 and d=152.
This code was found by Heurico 1.16 in 0.278 seconds.