The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+156x^65+272x^66+440x^67+520x^68+540x^69+427x^70+428x^71+474x^72+366x^73+297x^74+82x^75+38x^76+24x^77+8x^78+8x^79+6x^80+1x^82+1x^86+1x^88+2x^89+2x^91+2x^94

The gray image is a code over GF(2) with n=560, k=12 and d=260.
This code was found by Heurico 1.16 in 0.875 seconds.