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  X  1  1  1
 0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2 2X  2 2X  2 2X  2 2X  2  0 2X+2 2X  2 2X  2 2X  2  0 2X+2 2X  2 2X  2 2X  2 2X 2X+2  0  2 2X  2 2X  2  0 2X 2X+2  2 2X  2 2X  2  0 2X+2 2X+2  0  0  0
 0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X  0 2X 2X 2X  0  0  0  0  0  0  0  0 2X
 0  0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X 2X 2X  0  0 2X 2X  0 2X  0 2X  0  0  0  0  0  0 2X 2X
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X 2X 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X  0  0  0  0 2X 2X  0
 0  0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  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+10x^66+31x^68+128x^69+684x^70+128x^71+31x^72+9x^74+1x^76+1x^138

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 0.359 seconds.