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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+56x^63+95x^64+96x^65+39x^66+128x^67+280x^68+128x^69+48x^71+64x^72+32x^73+24x^74+8x^76+24x^79+1x^130

The gray image is a code over GF(2) with n=272, k=10 and d=126.
This code was found by Heurico 1.16 in 90.1 seconds.