The generator matrix

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

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+288x^65+519x^66+672x^67+517x^68+410x^69+404x^70+512x^71+380x^72+216x^73+75x^74+44x^75+13x^76+14x^77+9x^78+4x^79+16x^81+1x^94+1x^96

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 1.03 seconds.