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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+150x^60+8x^61+122x^62+88x^63+154x^64+256x^65+112x^66+336x^67+132x^68+232x^69+92x^70+88x^71+126x^72+16x^73+48x^74+58x^76+10x^78+14x^80+4x^84+1x^112

The gray image is a code over GF(2) with n=268, k=11 and d=120.
This code was found by Heurico 1.16 in 1.1 seconds.