The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1 X^2+2  1  1  0  1  X  1
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X X^2+2 X^2 X^2+X+2 X^2+X  0  2  X X^2+2  2  0  X X^2+2 X^2+2  X  X X^2+X+2  0
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X+2  X  2  0 X^2+X X+2 X^2+2  2 X^2+X+2 X^2 X^2 X+2 X^2+2 X^2+X  X X^2+X X^2+X+2 X+2 X^2  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+51x^26+164x^27+210x^28+216x^29+198x^30+112x^31+44x^32+8x^33+6x^34+12x^35+1x^40+1x^50

The gray image is a code over GF(2) with n=232, k=10 and d=104.
This code was found by Heurico 1.16 in 0.016 seconds.