The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 1 1 X 0 1 1 X X 1 X X 1 X 2 X 2 X 0 X X X X 1 1 2 2 1 1 X X 1 1 1 1 1
0 X 0 X+2 0 X+2 0 X 2 X+2 2 X 2 X+2 2 X 0 X+2 X+2 X X+2 X 0 X+2 X+2 X 2 X 0 2 2 0 2 X X X X X X+2 X 0 2 X X 0 2 X X 0 2 0 2 X+2 X+2 X X 0
0 0 2 0 0 2 2 2 2 0 2 0 0 2 0 2 0 0 0 2 2 0 0 0 2 2 0 0 2 2 0 2 2 0 2 2 2 2 0 0 0 0 0 0 2 2 0 0 2 2 0 0 2 2 2 2 0
0 0 0 2 2 2 2 0 0 0 2 2 2 0 0 2 0 0 2 2 0 0 2 2 2 0 2 2 2 2 0 0 0 0 0 2 2 0 0 2 2 2 2 0 2 2 2 0 0 0 0 0 2 0 0 2 0
generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.
Homogenous weight enumerator: w(x)=1x^0+14x^56+92x^57+14x^58+1x^64+4x^65+2x^66
The gray image is a code over GF(2) with n=228, k=7 and d=112.
This code was found by Heurico 1.16 in 0.0923 seconds.