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  1  1  1  X  1  X  X  X
 0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X+2 2X 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X  2 2X+2 2X 2X 2X+2 2X 2X+2  0  2 2X 2X+2 2X 2X+2 2X 2X+2  0  2  0  2  0 2X  2 2X+2  0  0  0  2  2  2  2 2X
 0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0 2X  0 2X  0 2X  0  0 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X
 0  0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0  0  0  0  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0  0  0  0
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0  0 2X 2X 2X  0  0  0  0  0 2X 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X
 0  0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X  0  0  0 2X  0  0 2X 2X  0 2X  0 2X 2X 2X 2X 2X  0  0  0  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+44x^76+16x^77+42x^78+48x^79+719x^80+48x^81+52x^82+16x^83+32x^84+2x^86+3x^88+1x^152

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 0.562 seconds.