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

generates a code of length 73 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+337x^68+24x^69+562x^70+272x^71+568x^72+704x^73+556x^74+240x^75+446x^76+40x^77+230x^78+78x^80+24x^82+8x^84+4x^86+1x^88+1x^124

The gray image is a code over GF(2) with n=584, k=12 and d=272.
This code was found by Heurico 1.16 in 0.703 seconds.