The generator matrix

 1  0  0  0  1  1  1  2  0  1  1  0  2  1  1  2  1  0  X  1  1  1  1  X  1  1  1 X+2 X+2  1  1  1  X  0  1  1 X+2 X+2  1  1  1  2  1  2 X+2 X+2 X+2  1  1  X  X  2  1  0  2 X+2 X+2  X  X  1  1  X X+2  0  1  2  1
 0  1  0  0  0  1  1  1  2  X X+2  1  1 X+1 X+1 X+2  X X+2  2  0 X+2  1  X  1  3 X+3  3  1  1  X  3 X+3  X  1  2 X+1  0 X+2 X+2  2  2  1 X+1  2  1  2  1 X+1  1  1  1  1  3  2  2  1  X  1  0  2 X+3  1  1  1  X  1  0
 0  0  1  0  1  2  3  1  1  0 X+3  1  2 X+1 X+2  1  2  X  1 X+3 X+2  X  3 X+3  1  3  0 X+2 X+1  1 X+1 X+1  1  2 X+1  X  1  2  0 X+1  3 X+3  3  1  1  2  2  2 X+2  3 X+2  1 X+3  1 X+2  X X+2  1  1 X+3  X X+2  2 X+1  X  0 X+2
 0  0  0  1  2  0  2  2  1  1  3  3  3  1  3  X  X  1  3 X+3 X+1  X  0  3 X+2 X+3 X+3 X+1  2 X+1  3  X  3 X+2  2  2  0  1  2 X+2 X+1 X+3  1 X+2  3  1  X  0  1  X X+2 X+2  2  0  1  0  1  0  X  3 X+2 X+1 X+1  2  X X+1  3

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+162x^61+306x^62+350x^63+501x^64+436x^65+333x^66+320x^67+298x^68+336x^69+244x^70+224x^71+186x^72+116x^73+98x^74+58x^75+62x^76+22x^77+10x^78+22x^79+8x^80+1x^82+2x^83

The gray image is a code over GF(2) with n=268, k=12 and d=122.
This code was found by Heurico 1.11 in 0.381 seconds.