The generator matrix

 1  0  1  1  1  2  X  1  1  1 X+2  1  1  1  1  0  1  0  1  1  X  1  1  X  1  1  1  0  1 X+2  1  1  2  X  1  1  1  1  0  X  1  1  1  X  1  0  X  1  1  X  X  1  1  1  1  1  1  X  1  X  1  1  1  1  1  X  2
 0  1  1 X+2 X+3  1  1 X+1  X  3  1 X+2 X+2  2 X+1  1 X+1  1  2  1  1  2  1  1  0 X+2 X+1  1  0  1 X+1 X+3  1  1  1  2  X  3  1 X+2  0  X  X  1 X+1  1  1  1  1  X  X  0  0  X X+2  0  0  2  2 X+2  2  2  2  2  X  0  1
 0  0  X  0 X+2  X  X  2  X  2  0  0 X+2  X  2  0  X X+2  0 X+2  0 X+2  2 X+2  0  2  0  2  2  2  0  X X+2  X  X X+2  X  2  0  2 X+2  X  0  X X+2 X+2  0 X+2  2 X+2  2  0 X+2  0  2  X X+2  X  2  X  X X+2  2  0 X+2 X+2  X
 0  0  0  2  0  2  2  2  0  2  0  2  0  2  0  2  2  0  0  2  2  2  0  0  2  0  0  2  2  0  2  0  2  2  0  0  2  2  0  2  0  2  0  0  2  0  2  2  0  2  2  0  2  2  2  2  2  0  0  2  2  0  2  2  2  2  2
 0  0  0  0  2  2  0  0  2  2  2  2  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  2  0  0  2  0  0  2  2  2  2  0  2  2  0  0  0  2  2  0  0  0  2  2  2  2  0  2  2  2  2  0  2  0  0  0  0  2  0  0  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+44x^62+118x^63+114x^64+132x^65+141x^66+76x^67+102x^68+64x^69+40x^70+102x^71+26x^72+8x^73+26x^74+4x^75+6x^76+2x^78+4x^80+4x^81+2x^82+4x^83+2x^84+1x^88+1x^90

The gray image is a code over GF(2) with n=268, k=10 and d=124.
This code was found by Heurico 1.16 in 0.227 seconds.