The generator matrix

 1  0  0  1  1  1  2  1  1  1  1 X^2+X+2 X+2 X^2+X  1  1  1 X+2  1 X^2 X^2+X  1  1  1  0  1  X X^2+X  1  1 X^2+2 X^2+X+2 X^2+2  2 X^2+X  1  1  1 X^2  1 X^2+X X^2  1  1  1  1  X  1  1  1  1 X^2  1 X^2+X  1  0 X+2  1  1  1 X+2  X  1 X^2+2 X^2+X+2  2  1  1  1
 0  1  0 X^2 X^2+3 X^2+1  1 X+2  2 X+1 X^2+X+3  1 X^2  1 X^2+X+2 X+3 X^2+X+2 X^2+X+2 X^2+X+3  1  1  1  2 X^2+3  X X^2+X  1  1  2 X^2+X+1 X^2  1  1  1 X^2+X+2 X+1  X X^2+3  1 X^2+X  1  1 X+2  1  X  0  1  2  1 X^2 X+3  1 X^2+3  1 X^2  1 X^2  1 X+3 X+2  1  0 X^2+X+1  1 X^2+X+2 X^2+X  3  3  0
 0  0  1 X^2+X+1 X^2+X+3 X^2+2 X+1 X^2+X+2 X^2+3  2 X^2+1 X^2+X+3  1  0 X^2+2  X X+1  1 X+1 X^2+3 X^2+X  3 X^2+X X^2+X+2  1  1 X+2  1 X^2  0  1  0 X^2+X+2 X^2+1  1 X^2+3 X^2+X+3 X+2  2 X^2+1 X^2+1 X+2 X^2+X X^2+X+1  X X^2+1 X+1 X^2+X X^2+1 X^2+X+3 X^2+X+1 X+3 X^2+X+2  X  2 X^2  1  2 X^2+X X^2+2  0  1 X^2 X^2+X+2  1  1 X+2 X^2+X  0
 0  0  0  2  2  2  0  2  0  0  0  2  2  2  0  0  2  0  0  0  2  2  2  0  0  0  0  0  2  2  2  0  2  2  2  2  0  2  2  2  2  2  0  0  2  2  0  0  0  0  2  0  2  0  2  2  0  0  2  2  2  2  2  0  2  0  0  2  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+80x^64+702x^65+867x^66+1280x^67+831x^68+1362x^69+749x^70+772x^71+482x^72+414x^73+291x^74+260x^75+8x^76+66x^77+11x^78+8x^79+5x^80+2x^82+1x^84

The gray image is a code over GF(2) with n=552, k=13 and d=256.
This code was found by Heurico 1.16 in 0.796 seconds.