The generator matrix

 1  0  0  1  1  1  0  X  1  1  1  1 X^2+X+2  2  X  1  1 X^2+2  1  1  1  1  1  1  1  1  1 X+2  1
 0  1  0 X^2 X^2+1  1  1  X X^2+1  3  0 X^2+2  2  1  1 X+2 X^2+X+3  1 X^2+X+1 X^2+X+1  X X^2  3 X^2+X X^2+1 X+3 X+3  1  0
 0  0  1 X^2+X+1 X+1 X^2 X+1  1 X^2+1 X+2 X^2+X  3  1 X^2+X+2  3 X^2+X X^2+3 X^2+2 X^2+X+3  2  3  1  0  X X^2+X+1 X^2+X  0  X  0
 0  0  0  2  2  0  2  2  0  2  2  0  2  0  0  2  0  2  2  0  0  2  2  0  0  0  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+150x^25+595x^26+1246x^27+1352x^28+1736x^29+1260x^30+1064x^31+478x^32+190x^33+81x^34+18x^35+8x^36+12x^37+1x^40

The gray image is a code over GF(2) with n=232, k=13 and d=100.
This code was found by Heurico 1.16 in 0.25 seconds.