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

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+111x^60+4x^61+200x^62+52x^63+223x^64+120x^65+292x^66+152x^67+262x^68+132x^69+166x^70+52x^71+133x^72+56x^74+50x^76+22x^78+18x^80+1x^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 0.428 seconds.