The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+104x^67+632x^68+784x^69+578x^70+510x^71+419x^72+364x^73+191x^74+162x^75+154x^76+64x^77+92x^78+28x^79+9x^80+1x^82+1x^84+1x^86+1x^90

The gray image is a code over GF(2) with n=568, k=12 and d=268.
This code was found by Heurico 1.16 in 0.282 seconds.