The generator matrix

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

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+364x^67+258x^68+1068x^69+223x^70+642x^71+233x^72+700x^73+104x^74+272x^75+31x^76+84x^77+38x^78+58x^79+4x^80+4x^81+1x^82+8x^83+1x^86+1x^90+1x^92

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 0.844 seconds.