The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  X  1  1 X^2+X  1  1 X^2+2  1  1  2  1  1  1  2 X^2+X  1  1  1  X  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+X+2 X^2+X+1  1  X X+1  1 X^2+2  3  1  2 X^2+3  1 X+2 X^2 X^2+X+3  1  1  1  0  0 X^2+X+2  0 X+2
 0  0 X^2  0  2 X^2+2 X^2+2 X^2+2 X^2 X^2  2  0  0  2  0 X^2 X^2+2 X^2  2 X^2  0 X^2  2 X^2+2  2  0 X^2 X^2  0
 0  0  0  2  2  2  0  2  0  2  0  2  2  0  2  0  0  0  0  2  2  2  0  2  2  2  2  2  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+190x^26+192x^27+536x^28+256x^29+500x^30+192x^31+153x^32+14x^34+12x^36+2x^40

The gray image is a code over GF(2) with n=232, k=11 and d=104.
This code was found by Heurico 1.16 in 0.032 seconds.