The generator matrix

 1  0  0  1  1  1  2  1  1 X+2  1  1  0  2  0  X  1  1 X+2  1  1  X  1  1  X  2  1  0  1  0  X  1  1 X+2  1  1  X X+2  1  1  X  1  1  1 X+2  1  1  1 X+2  1  1  0  1  2  1  X  1 X+2  1  2  0  1  1 X+2  1  2 X+2  1
 0  1  0  2  3  1  1  0  2  0  3  1  1  1 X+2  X  X X+3  1 X+1 X+2  1 X+1 X+1  1  1  X  X  X  1  1  0  2  1 X+2  X  0  1  1  3  1 X+2  3  1  1 X+2 X+3 X+1 X+2 X+1 X+1  2 X+1  0 X+3 X+2  2  2  0  X  1  1 X+2  1 X+3  1  X  3
 0  0  1 X+3 X+1  2 X+1 X+2  1  1  3  X X+2  3  1  1  X  1  X  0  3 X+3 X+2 X+1  0 X+3  2  1 X+1  2  1  2  3 X+1  0  1  1  1 X+3 X+2  X  X  2  3  2 X+1  X X+3  1  X  3  1  1  1 X+3  1  0  1  3  1 X+3  1 X+3  0 X+1  2  1  3

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+62x^65+94x^66+110x^67+65x^68+82x^69+30x^70+12x^71+20x^72+9x^74+10x^75+2x^76+12x^77+1x^78+2x^86

The gray image is a code over GF(2) with n=272, k=9 and d=130.
This code was found by Heurico 1.13 in 0.094 seconds.