The generator matrix

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

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+122x^26+292x^27+531x^28+266x^29+464x^30+204x^31+111x^32+26x^33+5x^34+12x^35+12x^36+1x^38+1x^40

The gray image is a code over GF(2) with n=232, k=11 and d=104.
This code was found by Heurico 1.16 in 0.016 seconds.