The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+263x^60+24x^61+114x^62+140x^63+416x^64+284x^65+130x^66+548x^67+337x^68+612x^69+114x^70+308x^71+283x^72+100x^73+90x^74+28x^75+175x^76+4x^77+52x^78+51x^80+12x^82+9x^84+1x^104

The gray image is a code over GF(2) with n=272, k=12 and d=120.
This code was found by Heurico 1.16 in 12.6 seconds.