The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+116x^74+792x^75+500x^76+710x^77+482x^78+524x^79+184x^80+302x^81+138x^82+128x^83+45x^84+104x^85+23x^86+32x^87+12x^88+2x^92+1x^98

The gray image is a code over GF(2) with n=624, k=12 and d=296.
This code was found by Heurico 1.16 in 0.359 seconds.