The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  0  1  1  1  1  1  1  2  1  X  X  1  X  1  X  X  X  1  2  X  1  1 X^2+2  1  0  1
 0  X  0  X  2  0 X^2+X X^2+X+2  0  2 X+2  X  2 X^2+X+2  2 X^2+X+2  2 X^2+X X^2+X X^2 X+2 X^2+2 X^2+2 X^2+X  X X^2 X^2+2  X X^2+X+2  0  X  0 X^2+2  0 X^2+X  X X^2+2  2 X^2+X+2  X X^2  X X^2+X X^2+2  0 X^2+2 X^2  X  X X+2  2  X  X  X X+2 X^2+2 X+2 X^2+2 X^2+X+2 X^2 X^2+X  X X^2+X+2  X  X  X X^2+X
 0  0  X  X  0 X^2+X+2 X^2+X  2 X^2 X^2+X+2 X^2+X+2 X^2 X+2 X^2 X^2+2  X  2  2 X^2+X  X X^2 X^2+X  2 X^2+X X^2+X X+2  0 X^2  2  2 X+2  X  2 X^2+X X+2 X+2 X+2 X^2  0  0  X X^2+2  X  2  X X^2+2 X^2  0 X^2+X+2 X^2+2 X^2+X  0 X^2+X+2 X^2+2  X X^2+X  X X+2 X+2  X  2  2 X^2 X^2+2  X X^2+X  0
 0  0  0 X^2 X^2 X^2+2  0 X^2+2 X^2  2 X^2+2  0 X^2 X^2+2  0  2  2  0  2  0 X^2 X^2+2 X^2 X^2+2  0  2  0 X^2+2  2 X^2+2 X^2+2 X^2+2 X^2+2  0 X^2  2  2  2 X^2  2 X^2+2 X^2+2  0  2  2 X^2  2 X^2 X^2  2 X^2 X^2+2  2  0  0 X^2+2 X^2+2 X^2+2 X^2+2  2 X^2+2  0  2  2  0  2 X^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+294x^62+32x^63+591x^64+288x^65+726x^66+424x^67+736x^68+216x^69+358x^70+56x^71+216x^72+8x^73+122x^74+23x^76+4x^78+1x^108

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 8.58 seconds.