The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+182x^61+371x^62+608x^63+670x^64+690x^65+815x^66+680x^67+695x^68+650x^69+544x^70+576x^71+516x^72+358x^73+307x^74+210x^75+115x^76+80x^77+35x^78+52x^79+19x^80+8x^81+8x^82+2x^83

The gray image is a code over GF(2) with n=272, k=13 and d=122.
This code was found by Heurico 1.16 in 3.25 seconds.