The generator matrix

 1  0  1  1 X^2  1 X^2+2  1  1  1  1  0  1  1 X^2  1  1  0 X+2  1  1 X^2+X  1 X^2  1  1  X X^2+X  1
 0  1  1 X^2+X  1 X^2+X+1  1 X^2 X^2+X+3  X  3  1  0 X+1  1 X^2+X X^2+1  1  1 X+2 X+2  1 X+3  1 X^2+X+1 X^2+3 X^2+X+2  1 X+1
 0  0  X  0 X+2  X X^2+X+2 X+2  2 X+2  2 X^2+2 X^2+2 X^2 X^2 X^2+2 X^2 X^2+X X^2+X X^2+X+2  2  2 X+2 X+2 X^2+X+2 X^2 X+2 X^2+2 X^2+X+2
 0  0  0  2  0  2  2  2  0  0  2  2  0  0  0  2  2  0  2  2  0  2  0  2  0  0  2  0  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+437x^26+384x^27+968x^28+656x^29+874x^30+352x^31+324x^32+16x^33+65x^34+18x^36+1x^40

The gray image is a code over GF(2) with n=232, k=12 and d=104.
This code was found by Heurico 1.16 in 109 seconds.