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

generates a code of length 71 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+136x^67+107x^68+308x^69+281x^70+474x^71+311x^72+224x^73+19x^74+68x^75+45x^76+60x^77+3x^78+10x^79+1x^130

The gray image is a code over GF(2) with n=568, k=11 and d=268.
This code was found by Heurico 1.16 in 0.437 seconds.