The generator matrix

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

generates a code of length 69 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+89x^64+300x^65+470x^66+530x^67+502x^68+424x^69+480x^70+516x^71+392x^72+206x^73+100x^74+52x^75+7x^76+8x^77+4x^78+4x^79+4x^81+2x^83+1x^84+1x^86+2x^89+1x^94

The gray image is a code over GF(2) with n=552, k=12 and d=256.
This code was found by Heurico 1.16 in 0.438 seconds.