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

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

Homogenous weight enumerator: w(x)=1x^0+43x^68+32x^69+36x^70+9x^72+4x^74+1x^76+2x^80

The gray image is a code over GF(2) with n=276, k=7 and d=136.
This code was found by Heurico 1.16 in 0.143 seconds.