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  0  1  0  0  1  X  1  1  1  X  1  X  0  2  1  X  1  1  1  X  1  0  1  1  0  1  X  1  X  1  X  1  0  X  X
 0  X  0  X  0  0  X X+2  0  2 X+2  X  0  X  X  2  2  0  X X+2  0  0 X+2 X+2  2 X+2  X  2  2  X  X  0 X+2  X  0  2  0  X  X  0  0  2  0 X+2 X+2  X  X  2  X  2  2  2  2  X  X  0  X  X  0  2  2 X+2  2  X  X  X X+2  2
 0  0  X  X  0 X+2  X  0  2  X  0  X  0 X+2  2 X+2  X  0  X  2 X+2  0  2  X  2  X  2  0  X X+2  2 X+2  0  0  X  X  X  2  X  X X+2  2 X+2 X+2  0  0 X+2  X  X  0 X+2 X+2  X  X  2  2  X  2  2  X X+2  0  0  X  0  2 X+2  0
 0  0  0  2  0  0  0  0  2  2  2  0  2  2  2  2  2  0  2  2  2  2  2  2  2  2  0  0  2  2  0  0  2  2  2  0  2  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  0  0  0  2  2  2  2  2  0  2  0  2  0  2  2  0  0  0  0  2  2  0  0  0  0  2  0  0  2  0  0  2  2  2  2  2  0  2  2  0  2  2  2  0  0  0  2  2  2  0  0  2  2
 0  0  0  0  0  2  0  0  0  2  0  2  2  0  2  0  2  0  0  2  2  0  0  0  0  2  2  2  2  0  0  2  0  2  2  2  0  2  2  0  0  2  2  0  0  2  0  0  2  0  0  2  0  0  0  2  2  2  2  0  0  2  0  0  2  0  0  2
 0  0  0  0  0  0  2  0  2  2  2  2  2  0  2  2  0  2  2  0  2  0  0  2  0  2  2  2  2  2  2  0  0  0  0  2  0  2  0  0  2  0  0  2  0  2  2  0  0  2  0  2  0  0  2  0  2  2  0  0  2  0  0  0  0  2  0  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  0  2  0  2  0  0  2  0  2  2  0  0  2  2  0  2  2  2  0  2  2  0  2  0  0  2  2  0  2  0  2  2  0  0  0  0  0  0  2  2  0  2  0  2  2  2  2  0  2  0  2  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+276x^60+182x^62+650x^64+548x^66+883x^68+596x^70+495x^72+160x^74+192x^76+38x^78+49x^80+12x^82+8x^84+5x^88+1x^100

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 seconds.