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

generates a code of length 77 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+132x^75+209x^76+404x^77+152x^78+76x^79+21x^80+28x^81+1x^148

The gray image is a code over GF(2) with n=616, k=10 and d=300.
This code was found by Heurico 1.16 in 60.8 seconds.