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

generates a code of length 79 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+38x^76+112x^77+217x^78+300x^79+226x^80+88x^81+20x^82+12x^83+6x^84+3x^86+1x^152

The gray image is a code over GF(2) with n=632, k=10 and d=304.
This code was found by Heurico 1.16 in 0.704 seconds.