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

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

Homogenous weight enumerator: w(x)=1x^0+261x^66+168x^67+569x^68+232x^69+767x^70+240x^71+701x^72+240x^73+510x^74+104x^75+169x^76+40x^77+61x^78+30x^80+2x^84+1x^122

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 23.5 seconds.