The generator matrix

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

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+121x^66+292x^67+361x^68+560x^69+548x^70+572x^71+418x^72+448x^73+339x^74+236x^75+97x^76+48x^77+8x^78+20x^79+11x^80+6x^82+6x^84+2x^86+2x^100

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 0.562 seconds.