The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 1 1 X 0 X 0 1 1 1 X X X 1 X X X X X X X 1 1 1 1 2 2 2 2 X X 1 1 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+2 X X+2 X 0 0 0 2 2 2 X 0 0 X X X X 0 2 2 2 2 X X X X 0 2 X+2 X+2 0
0 0 2 0 0 2 2 2 2 0 2 0 0 2 0 2 0 0 2 2 0 0 0 2 2 0 0 2 2 2 2 0 2 0 2 2 0 2 0 2 2 2 0 0 2 2 0 0 0 0 0 2 0
0 0 0 2 2 2 2 0 0 0 2 2 2 0 0 2 0 2 2 0 0 0 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 0 2 2 0 0 2 2 0 0 0 2 2 0
generates a code of length 53 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.
Homogenous weight enumerator: w(x)=1x^0+36x^52+64x^53+12x^54+10x^56+4x^62+1x^64
The gray image is a code over GF(2) with n=212, k=7 and d=104.
This code was found by Heurico 1.16 in 0.0703 seconds.