The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+384x^75+270x^76+344x^77+206x^78+296x^79+175x^80+240x^81+50x^82+60x^83+12x^85+4x^89+4x^91+2x^112

The gray image is a code over GF(2) with n=624, k=11 and d=300.
This code was found by Heurico 1.16 in 0.422 seconds.