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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+8x^65+28x^66+56x^67+326x^68+56x^69+28x^70+8x^71+1x^136

The gray image is a code over GF(2) with n=272, k=9 and d=130.
This code was found by Heurico 1.16 in 0.156 seconds.