The generator matrix

 1  0  0  1  1  1  0  1  2  1  1  2  1  2 X+2  1  1  1 X+2  1  X X+2  1  2  1  2  1 X+2  1 X+2  0  1  1  0  0 X+2  X  1  2  1  1  1  1 X+2  2  1  X  1  1  1  1  1  1  1  0  2  1  X X+2  1  1  1  0 X+2  2  1  1  1
 0  1  0  0  1  3  1  X  1  1  2  1 X+1 X+2  1 X+3  X X+1  0 X+2  1  1 X+3  0  X  1 X+1  1  2  2  1  1  0  2  1  X  1  2  1  1  3  2 X+3  1  X X+1  1 X+2 X+2 X+1  3  3  0  0  X  1  X X+2  1  3 X+1  3  1  0  2 X+2  0  1
 0  0  1 X+1 X+3  0 X+1  1  X  1  X  3  0  1  X X+2 X+1 X+3  1  X  1 X+1  2  1 X+1  2  1  2 X+2  1  1 X+2  3  1  X  1  2 X+1 X+3  0 X+3  X X+3  1  1  0 X+1  3  0  3  0  1  1  3  1 X+3  1  1 X+1 X+1  1 X+2  1  1  X  3  X X+1
 0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  0  2  0  0  2  2  0  2  0  0  0  2  2  2  0  0  0  0  2  0  2  2  0  2  0  2  2  2  0  0  2  0  0  0  2  2  2  2  0  0  2  0  2  0  2  2  0  0
 0  0  0  0  2  2  2  0  2  2  0  2  2  0  2  0  2  0  2  2  0  0  0  2  2  0  0  2  0  2  2  0  0  2  0  2  2  0  2  0  0  2  0  0  0  0  2  0  2  2  2  0  2  0  0  0  2  2  0  0  0  2  0  0  2  2  2  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+188x^63+125x^64+372x^65+113x^66+312x^67+106x^68+260x^69+60x^70+180x^71+53x^72+116x^73+14x^74+40x^75+28x^76+40x^77+4x^78+16x^79+4x^80+8x^81+1x^82+2x^84+4x^85+1x^88

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 0.554 seconds.