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  1  X  1  1 2X+2  1  1 2X+2  1  1  1
 0  2  0  0  0 2X+2  2 2X+2  0  0  0 2X 2X+2  2 2X+2 2X+2  2 2X+2  2  2 2X  0 2X 2X 2X+2  0 2X 2X+2  0 2X+2  2 2X 2X+2 2X+2 2X+2  0  0 2X  0 2X+2  2 2X+2  2 2X 2X 2X+2  0  2  0 2X  0 2X  2 2X  0 2X+2 2X  2  2 2X+2  0  2 2X+2 2X+2  2 2X  2  0  2  2 2X+2
 0  0  2  0 2X+2 2X+2  2  0 2X+2  0  0 2X+2 2X+2 2X+2 2X 2X  2  2  0  0  2 2X  0  2 2X  2 2X  2  0  2 2X 2X+2  2  0  0 2X+2 2X  2 2X  2  0 2X+2  2 2X+2 2X  0  2  0  0 2X  2 2X+2 2X 2X 2X 2X+2 2X+2 2X 2X+2  0  0 2X 2X+2  2 2X+2  0  2 2X+2  2 2X  2
 0  0  0  2 2X+2  0  2 2X+2 2X+2  0  2  0 2X  2  2  0 2X  2  2 2X 2X  0  2  2  2 2X+2 2X  2 2X+2 2X  0  0 2X+2 2X+2  0  2 2X  0  2 2X 2X 2X+2  0 2X+2  0  2 2X 2X+2 2X+2 2X+2  0 2X+2  2  2 2X 2X+2 2X 2X 2X 2X 2X  0 2X 2X+2 2X+2 2X  2 2X+2  0  0  0
 0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X 2X 2X  0 2X  0  0  0  0  0  0  0  0 2X  0 2X  0  0 2X  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+137x^66+51x^68+160x^69+338x^70+704x^71+310x^72+160x^73+102x^74+21x^76+58x^78+5x^82+1x^136

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 56 seconds.