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

generates a code of length 32 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+104x^29+129x^30+206x^31+192x^32+184x^33+84x^34+72x^35+38x^36+8x^37+3x^38+2x^39+1x^48

The gray image is a code over GF(2) with n=256, k=10 and d=116.
This code was found by Heurico 1.16 in 0.016 seconds.