The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1  1  1  1  0  X  X  0  X  X
 0  X 2X+2 X+2  0 X+2 2X+2 3X X+2  0 3X 2X+2 3X 2X  2 3X+2 3X  0 X+2 2X+2 X+2  0 2X+2 3X 3X+2  0 3X 2X+2 3X+2 2X  X  2 X+2  0  0  X 2X+2 2X+2 3X+2  X 2X  2 X+2 X+2  2 2X 3X 3X  0 2X  0 2X X+2 3X+2 X+2 3X+2 2X+2 2X+2  2  2 2X 3X 3X  X  X  X X+2 3X  X  0  0
 0  0 2X  0  0  0 2X  0 2X  0 2X 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X 2X 2X  0 2X  0  0 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0  0  0  0  0 2X  0
 0  0  0 2X  0  0  0  0  0  0  0  0  0  0  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0  0 2X  0 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0  0  0 2X 2X  0
 0  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X 2X  0 2X  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0 2X  0 2X 2X  0 2X 2X  0 2X  0 2X 2X  0  0 2X  0  0 2X  0 2X 2X  0  0  0 2X 2X  0  0  0 2X 2X  0  0
 0  0  0  0  0 2X  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0  0 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0  0 2X 2X  0  0  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+44x^66+318x^68+256x^69+328x^70+256x^71+510x^72+108x^74+194x^76+32x^78+1x^128

The gray image is a code over GF(2) with n=568, k=11 and d=264.
This code was found by Heurico 1.16 in 0.438 seconds.