The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+29x^64+66x^65+76x^66+92x^67+76x^68+48x^69+34x^70+22x^71+16x^72+14x^73+15x^74+12x^75+4x^76+2x^78+2x^79+2x^80+1x^106

The gray image is a code over GF(2) with n=272, k=9 and d=128.
This code was found by Heurico 1.16 in 0.151 seconds.