The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 X X 0 X 2 2 X X X
0 X 0 X+2 0 X+2 0 X 2 X+2 2 X 2 X+2 2 X X+2 X X+2 X 0 X+2 X X X 0 2 0 2
0 0 2 0 0 2 2 2 2 0 2 0 0 2 0 2 0 0 2 2 2 0 0 0 0 2 2 2 0
0 0 0 2 2 2 2 0 0 0 2 2 2 0 0 2 0 2 2 0 2 2 0 0 2 0 2 0 0
generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+92x^28+31x^32+4x^36
The gray image is a code over GF(2) with n=116, k=7 and d=56.
This code was found by Heurico 1.16 in 0.0148 seconds.