The generator matrix

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

generates a code of length 67 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+238x^62+280x^63+440x^64+312x^65+676x^66+400x^67+561x^68+272x^69+393x^70+216x^71+163x^72+56x^73+68x^74+19x^76+1x^118

The gray image is a code over GF(2) with n=536, k=12 and d=248.
This code was found by Heurico 1.16 in 1.33 seconds.