The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^76+352x^77+284x^78+348x^79+217x^80+264x^81+136x^82+240x^83+45x^84+56x^85+24x^86+20x^87+9x^88+4x^90+4x^92+1x^108+1x^112

The gray image is a code over GF(2) with n=640, k=11 and d=304.
This code was found by Heurico 1.16 in 0.391 seconds.