The generator matrix

 1  0  1  1  1  2 X^2+X  1  1  1 X^2+X+2  1  1  1  1  1  X  1 X^2  1  X  1  1  1  1  1  1  1  1
 0  1 X+1 X^2+X+2 X^2+1  1  1  2 X^2+3 X^2+X  1  3 X^2+X+1 X+1 X^2+X+3 X^2+3 X+2 X^2  1  X  1  3  3 X+3 X+3 X^2+1  0 X^2+X+3  0
 0  0 X^2 X^2+2  2 X^2  0 X^2 X^2+2  0 X^2+2  2 X^2+2  0  2 X^2 X^2+2 X^2+2 X^2+2 X^2 X^2 X^2+2 X^2 X^2+2  2  0 X^2+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+36x^26+136x^27+280x^28+200x^29+216x^30+88x^31+18x^32+24x^33+20x^34+3x^36+1x^40+1x^44

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.