The generator matrix

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

generates a code of length 69 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+128x^65+544x^66+776x^67+707x^68+568x^69+348x^70+252x^71+215x^72+252x^73+132x^74+20x^75+88x^76+44x^77+8x^78+8x^79+2x^80+3x^84

The gray image is a code over GF(2) with n=552, k=12 and d=260.
This code was found by Heurico 1.16 in 0.266 seconds.