The generator matrix

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

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+160x^26+994x^27+472x^28+1104x^29+369x^30+654x^31+150x^32+140x^33+31x^34+20x^35+1x^36

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 0.062 seconds.