The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+78x^66+310x^67+506x^68+442x^69+561x^70+488x^71+461x^72+396x^73+447x^74+212x^75+97x^76+56x^77+16x^78+12x^79+2x^80+2x^83+2x^84+2x^85+2x^88+1x^90+1x^92+1x^94

The gray image is a code over GF(2) with n=568, k=12 and d=264.
This code was found by Heurico 1.16 in 0.469 seconds.