The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 1 X X X X 2 2 2 0 0 0
0 2 0 2 0 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 2 2 0
0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 0 2 2
generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 29.
Homogenous weight enumerator: w(x)=1x^0+16x^29+8x^30+7x^32
The gray image is a code over GF(2) with n=116, k=5 and d=58.
This code was found by Heurico 1.16 in 0.00546 seconds.