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

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

Homogenous weight enumerator: w(x)=1x^0+32x^69+20x^70+6x^72+4x^74+1x^80

The gray image is a code over GF(2) with n=276, k=6 and d=138.
This code was found by Heurico 1.16 in 0.142 seconds.