The generator matrix

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

generates a code of length 67 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+450x^61+1123x^62+2154x^63+3284x^64+3152x^65+4606x^66+3870x^67+4442x^68+3346x^69+2774x^70+1554x^71+981x^72+536x^73+267x^74+118x^75+29x^76+36x^77+21x^78+16x^79+6x^80+1x^82+1x^84

The gray image is a code over GF(2) with n=536, k=15 and d=244.
This code was found by Heurico 1.16 in 10.1 seconds.