The generator matrix

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

generates a code of length 29 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+58x^25+169x^26+262x^27+372x^28+408x^29+326x^30+236x^31+119x^32+42x^33+26x^34+14x^35+4x^36+4x^37+6x^38+1x^42

The gray image is a code over GF(2) with n=232, k=11 and d=100.
This code was found by Heurico 1.16 in 0.047 seconds.