The generator matrix

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

generates a code of length 29 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+83x^26+88x^27+209x^28+336x^29+126x^30+88x^31+60x^32+31x^34+1x^36+1x^48

The gray image is a code over GF(2) with n=232, k=10 and d=104.
This code was found by Heurico 1.16 in 0.032 seconds.