The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+200x^68+280x^69+400x^70+504x^71+486x^72+528x^73+360x^74+464x^75+411x^76+216x^77+128x^78+56x^79+47x^80+8x^82+4x^84+2x^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 120 seconds.