The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  X  1  1  2  1  1  0  1  1  0  X  1  1  X X+2  1  1 X+2  2  X  1  1 X+2  1  1  1  0  1  1  X  0  2  1  2  1  2  2  1  X  1  X  1  1 X+2  1 X+2  0  1  1  1  1  1  1 X+2  1  1  1  X
 0  1  0  0  3 X+1  1  2  2 X+3  1  2  1  1  0  2  0  1  3  1  1 X+2  X  X  1 X+3 X+1  X  1  1 X+2  X  1 X+3 X+1 X+2 X+2  1  X  1  1  1  0  1  0  1 X+2  3 X+2 X+1  1  2 X+2  1  X  1  1  1  2 X+3  2  X  1  1  X  1  2  1
 0  0  1  1  3  2  3  1  0 X+1  0 X+3  2  1  2 X+3  1  3  X X+2  1  X X+3  1 X+3 X+2 X+1  1 X+1 X+2  X X+1 X+3  0  X X+2  1 X+3  1  X  1 X+3  X  2  X X+3  1 X+2  1  3  2  2  2  2  2 X+3  3  3 X+3  0  3  0  0  X X+1 X+1  2  3
 0  0  0  X  X  0  X  X  X  0  X  0  X  0  2  2  2  0  0  0  0 X+2 X+2  X  X X+2 X+2 X+2  X  X  X  X  0  X  2  2  0  2  0  2 X+2  0  2  X X+2  2 X+2  X  0 X+2 X+2 X+2 X+2  2  0  2  X X+2  X  2  2  0  2  2  0  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+106x^63+269x^64+260x^65+267x^66+142x^67+235x^68+164x^69+158x^70+78x^71+94x^72+56x^73+65x^74+50x^75+34x^76+12x^77+21x^78+24x^79+4x^80+4x^81+3x^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 1.16 in 0.311 seconds.