The generator matrix

 1  0  0  1  1  1  0  2  0  2  1  1  1  1  1  1  1  1 X^2+X X^2+X+2  1 X+2 X^2+X  1  1  1 X+2  X  1 X^2+2  1  1 X^2  0  1  2  1 X^2  1  1  2  1  1 X^2+2  1  X  1  1  1 X^2+X+2  1 X^2+X+2 X^2 X^2 X+2 X^2  1  1  X X^2+X X^2+X+2  1  2  1  1  1 X^2+X
 0  1  0  0 X^2+3 X^2+1  1 X^2+X  1  1 X^2+X X+1 X+2 X+3 X+3 X^2+X X^2+3  X  1 X^2+2  3  1  1  2  0 X^2+X+3  X  1 X^2+X+3  1 X^2+2 X+3  0  1  2  1 X+1 X^2+X+2 X^2  2  1  3 X+3  1  3  1  1 X^2+X  X  1  X  1 X^2+X+2 X^2+2  1  1  3 X^2+X  0 X^2+2  1 X^2+1  1 X+3  2  2 X^2
 0  0  1 X+1 X+3  2 X^2+X+1  1 X^2+X+2 X^2+1 X^2+X X^2+X+1  3 X^2+2 X^2+3 X^2 X+2 X^2+X+1  2  1 X^2+3 X+3 X^2+X  1 X+2 X^2+X  1  3  0 X^2+X+3 X+3  3  1 X^2+X+3 X^2 X^2  X  1  2 X^2+X+3 X+2  X X^2+X+3  1 X^2+2 X^2 X^2+X+1  0 X^2+X+3 X+2 X^2+3  3  1  1 X^2+X+1 X+2  3 X^2+X+1  1  1 X^2+3 X^2+3 X^2+1 X^2+X X+1 X^2+3  1
 0  0  0 X^2 X^2  0 X^2 X^2+2 X^2+2 X^2  2 X^2 X^2+2  0 X^2+2  0  2 X^2+2  2  0  0 X^2+2 X^2+2  2 X^2+2 X^2 X^2  2 X^2  0  2 X^2 X^2  2 X^2 X^2+2  0  2 X^2+2 X^2+2  0 X^2  0  0  2 X^2  0  2  2  0 X^2+2 X^2 X^2  2  2 X^2 X^2+2 X^2  2 X^2  0  2  0 X^2+2  2  0  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+698x^62+840x^63+2000x^64+1576x^65+2626x^66+1856x^67+2247x^68+1312x^69+1456x^70+536x^71+670x^72+248x^73+222x^74+32x^75+36x^76+18x^78+5x^80+4x^82+1x^84

The gray image is a code over GF(2) with n=536, k=14 and d=248.
This code was found by Heurico 1.16 in 435 seconds.