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

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

Homogenous weight enumerator: w(x)=1x^0+35x^68+2x^69+19x^70+4x^71+2x^73+1x^74

The gray image is a code over GF(2) with n=544, k=6 and d=272.
This code was found by Heurico 1.16 in 0.171 seconds.