The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^69+17x^70+2x^71+4x^72+2x^73+1x^74+2x^75+1x^80

The gray image is a code over GF(2) with n=552, k=6 and d=276.
This code was found by Heurico 1.16 in 0.219 seconds.