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

generates a code of length 69 over Z4[X]/(X^2+2) 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.