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

generates a code of length 71 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+63x^64+120x^67+32x^68+256x^69+567x^70+64x^71+536x^72+256x^73+32x^74+48x^75+24x^78+8x^80+24x^83+16x^86+1x^134

The gray image is a code over GF(2) with n=568, k=11 and d=256.
This code was found by Heurico 1.16 in 0.484 seconds.