The generator matrix

 1  0  0  1  1  1  2  0  1  1  2  1  1  0  1  1  2  1  1  2  0  0  1  1  X  1  2  1 X+2  1  0  1 X+2  0  1  1  1 X+2  0  1  0  1 X+2  1  1  1  1  X X+2  X  X  X X+2  1  1  X  2  1  1  1  1  X  1  2  1  1  1  1
 0  1  0  0  1  1  1  2  2  3  1  2  3  1  0  1  1  0  1  1  X  1  0  1  2  3  1  0  X  2  1  1  0 X+2  X  2 X+3  X  1  3  1 X+1  1 X+2 X+1  X X+3 X+2  0  1  1  1  1  0 X+2  1  1 X+1 X+2 X+2 X+2  2 X+2  1  X X+2  0  X
 0  0  1  1  2  3  1  1  0  2  3  1  3  0  0  2  0 X+1 X+3 X+3  1  X  X X+2  1 X+3 X+1  X  1 X+1  X X+2  1  1  3  X  2  1  0 X+2  X  1 X+3  3  0 X+3  1  1  1 X+2  2  0  X  3 X+1  3  3  3  X X+2  X  1  2  X  0  2  1 X+2
 0  0  0  X  0  X  X  X  X  X  0  0  0  X X+2 X+2  2  X  X  0  0 X+2  2  2 X+2  2 X+2  0 X+2  2  X  0  2  X  2 X+2 X+2  0 X+2  X  2  2 X+2 X+2  0  X X+2  X  X  0 X+2  2  X  2  2  X  2  X  X  0 X+2  0  0  0 X+2  2  2 X+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+120x^63+248x^64+256x^65+207x^66+234x^67+252x^68+158x^69+108x^70+96x^71+105x^72+74x^73+38x^74+30x^75+35x^76+30x^77+21x^78+16x^79+6x^80+10x^81+1x^82+1x^84+1x^86

The gray image is a code over GF(2) with n=272, k=11 and d=126.
This code was found by Heurico 1.11 in 0.212 seconds.