The generator matrix

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

generates a code of length 78 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+25x^72+242x^73+212x^74+530x^75+333x^76+538x^77+416x^78+582x^79+347x^80+410x^81+127x^82+158x^83+58x^84+86x^85+11x^86+10x^87+2x^88+4x^89+1x^90+1x^92+1x^94+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 0.562 seconds.