The generator matrix

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

generates a code of length 67 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+276x^64+424x^65+320x^66+228x^67+201x^68+312x^69+140x^70+44x^71+68x^72+12x^73+12x^74+4x^77+4x^80+1x^92+1x^96

The gray image is a code over GF(2) with n=536, k=11 and d=256.
This code was found by Heurico 1.16 in 0.281 seconds.