The generator matrix

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

generates a code of length 78 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+88x^73+441x^74+386x^75+550x^76+396x^77+625x^78+272x^79+566x^80+246x^81+271x^82+90x^83+78x^84+32x^85+23x^86+18x^87+2x^88+2x^93+2x^95+3x^96+2x^97+2x^101

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 0.75 seconds.