The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+216x^66+128x^67+182x^68+128x^69+736x^70+128x^71+182x^72+128x^73+216x^74+1x^76+1x^100+1x^104

The gray image is a code over GF(2) with n=560, k=11 and d=264.
This code was found by Heurico 1.16 in 0.265 seconds.