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.