The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  X  X  X  1  1  1  X  X  X  1  1  2  2  2  X  X  X  X  1  X  1  1  2  2  2  X 2X 2X 2X  0  0  0  2  X  X  1  X  1  1
 0 2X  0 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0
 0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X  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+32x^69+20x^70+5x^72+4x^74+2x^76

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 0.187 seconds.