The generator matrix

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

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+150x^61+278x^62+408x^63+426x^64+448x^65+393x^66+398x^67+288x^68+310x^69+213x^70+172x^71+144x^72+166x^73+93x^74+78x^75+56x^76+28x^77+22x^78+16x^79+5x^80+2x^81+1x^86

The gray image is a code over GF(2) with n=268, k=12 and d=122.
This code was found by Heurico 1.16 in 0.718 seconds.