The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+170x^62+256x^63+495x^64+340x^65+436x^66+378x^67+380x^68+338x^69+272x^70+200x^71+244x^72+166x^73+142x^74+74x^75+76x^76+30x^77+50x^78+4x^79+36x^80+6x^81+2x^82

The gray image is a code over GF(2) with n=272, k=12 and d=124.
This code was found by Heurico 1.16 in 0.733 seconds.