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

generates a code of length 77 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+51x^74+42x^75+270x^76+304x^77+267x^78+36x^79+47x^80+1x^82+2x^83+2x^84+1x^150

The gray image is a code over GF(2) with n=616, k=10 and d=296.
This code was found by Heurico 1.16 in 0.641 seconds.