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

generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+6x^68+100x^69+6x^70+1x^72+12x^73+1x^74+1x^82

The gray image is a code over GF(2) with n=552, k=7 and d=272.
This code was found by Heurico 1.16 in 0.297 seconds.