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

generates a code of length 78 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+41x^72+222x^73+241x^74+440x^75+448x^76+506x^77+544x^78+470x^79+403x^80+282x^81+137x^82+144x^83+50x^84+66x^85+30x^86+34x^87+22x^88+12x^89+2x^92+1x^120

The gray image is a code over GF(2) with n=624, k=12 and d=288.
This code was found by Heurico 1.16 in 0.828 seconds.