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

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

Homogenous weight enumerator: w(x)=1x^0+38x^76+96x^77+56x^78+256x^79+61x^80+368x^81+64x^82+32x^83+26x^84+16x^85+8x^86+1x^88+1x^136

The gray image is a code over GF(2) with n=640, k=10 and d=304.
This code was found by Heurico 1.16 in 0.563 seconds.