The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+174x^63+92x^64+220x^65+42x^66+118x^67+68x^68+102x^69+12x^70+64x^71+22x^72+50x^73+10x^74+24x^75+6x^76+10x^77+2x^79+1x^80+2x^81+2x^83+2x^84

The gray image is a code over GF(2) with n=268, k=10 and d=126.
This code was found by Heurico 1.16 in 22.3 seconds.