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

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

Homogenous weight enumerator: w(x)=1x^0+16x^66+55x^68+880x^70+55x^72+16x^74+1x^140

The gray image is a code over GF(2) with n=560, k=10 and d=264.
This code was found by Heurico 1.16 in 0.344 seconds.