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

generates a code of length 78 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+308x^73+174x^74+472x^75+350x^76+540x^77+484x^78+548x^79+350x^80+396x^81+174x^82+236x^83+20x^85+12x^87+1x^88+16x^89+12x^91+1x^92+1x^132

The gray image is a code over GF(2) with n=624, k=12 and d=292.
This code was found by Heurico 1.16 in 147 seconds.