The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2) 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 0.735 seconds.