The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+138x^62+164x^63+333x^64+196x^65+306x^66+188x^67+172x^68+44x^69+96x^70+100x^71+117x^72+44x^73+62x^74+20x^75+28x^76+4x^77+18x^78+8x^79+4x^80+4x^82+1x^88

The gray image is a code over GF(2) with n=268, k=11 and d=124.
This code was found by Heurico 1.16 in 0.303 seconds.