The generator matrix
1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 X X X X^2 X^2 X^2 X X 1 1 X^2 1
0 2 0 2 0 0 2 2 0 0 2 0 2 2 2 0 0 2 2 0 2 2 0 0 0 2 2 0 0
0 0 2 2 0 2 2 0 0 2 2 2 2 0 0 0 2 2 0 0 2 0 2 2 0 2 0 0 0
generates a code of length 29 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+3x^28+50x^29+3x^30+6x^33+1x^34
The gray image is a code over GF(2) with n=232, k=6 and d=112.
This code was found by Heurico 1.16 in 0.015 seconds.