The generator matrix

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

generates a code of length 70 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+662x^65+1058x^66+1898x^67+1820x^68+2242x^69+1820x^70+2230x^71+1413x^72+1336x^73+722x^74+562x^75+240x^76+220x^77+80x^78+42x^79+13x^80+18x^81+4x^83+2x^85+1x^88

The gray image is a code over GF(2) with n=560, k=14 and d=260.
This code was found by Heurico 1.16 in 373 seconds.