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

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

Homogenous weight enumerator: w(x)=1x^0+120x^68+3x^72+3x^80+1x^88

The gray image is a code over GF(2) with n=272, k=7 and d=136.
This code was found by Heurico 1.16 in 0.138 seconds.