The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  2  X  X  0  2  1  1 X^2+2  1  0  X  1
 0  X  0  X  0 X^2 X^2+X X^2+X X^2 X^2+2  0  X  2 X+2 X^2+X+2 X^2 X^2+X+2 X^2+2 X^2+X+2 X+2  X  X  0  2  X  2  X X^2+X X^2+X
 0  0  X  X X^2+2  X X^2+X  0 X^2 X^2+X  2 X^2+X+2 X^2+X+2 X^2+X+2 X^2 X^2+X+2 X^2  X X^2 X^2+X X^2+X X^2 X^2+X+2  X  0  X  2 X^2+X+2 X^2+X+2
 0  0  0  2  0  0  2  2  2  2  2  0  2  0  2  2  0  0  0  0  0  2  0  2  2  0  0  2  0
 0  0  0  0  2  2  2  2  0  2  2  2  0  0  0  2  2  2  0  0  2  2  0  2  0  2  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+178x^25+254x^26+664x^27+451x^28+1082x^29+516x^30+564x^31+114x^32+156x^33+62x^34+36x^35+9x^36+6x^37+1x^40+2x^41

The gray image is a code over GF(2) with n=232, k=12 and d=100.
This code was found by Heurico 1.16 in 41.2 seconds.