The generator matrix

 1  0  1  1  1 X^2+X  1  1  1 X^2+2  1 X+2  1  1  1  0  1  1  1 X^2+X  1  1  1  1 X^2+2  1  1 X^2+2 X+2
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3  3 X^2+2  1 X+2  1 X^2+1 X+1  0  1 X^2+X+3 X^2+X X^2+1  1 X^2+X+3 X^2+3  3 X^2+2  1 X^2+2 X^2+1  X  1
 0  0  2  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  2  0  2  0  2  0  2  2  0  0  0
 0  0  0  2  0  2  2  2  2  2  0  0  0  0  2  2  0  0  2  0  2  2  2  2  2  0  0  2  0
 0  0  0  0  2  0  2  2  0  0  0  0  2  2  0  0  2  0  2  0  0  2  0  2  2  2  0  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+213x^26+192x^27+430x^28+384x^29+440x^30+192x^31+173x^32+18x^34+2x^36+2x^40+1x^42

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 17.5 seconds.