The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 2 1 X 1 0 1 1 X 1 1 2 X 1 X 1 2 X 1 X 0 1
0 X 0 0 0 X X+2 X 2 2 X 0 0 X X X+2 0 0 X+2 X 2 X X+2 X 2 0 2 2 X+2 0 X X+2 X X+2 X+2 X X X 0 X+2 X+2 X X X+2 X+2 2 X+2 X 0 X+2 0 X X X 0 0 2 2
0 0 X 0 X X X 0 2 0 X+2 X X+2 0 X+2 0 2 X+2 2 X+2 0 2 X 0 X+2 X+2 X 2 X 2 0 X+2 X X 0 2 X+2 X X+2 2 X 2 X+2 X 0 0 X+2 X+2 X 2 0 X 0 2 0 X+2 X 0
0 0 0 X X 0 X X+2 0 X 2 X 2 X+2 X 0 2 X X 0 X+2 2 X+2 X+2 0 0 X+2 X X 0 0 0 0 0 2 2 2 2 X+2 2 X+2 2 X+2 2 2 X 0 0 X 0 X+2 2 X+2 X+2 X 2 2 X
0 0 0 0 2 0 0 0 2 2 2 2 0 2 0 2 2 0 0 0 2 0 2 2 2 2 0 0 2 0 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 2 0 0 0 0 0 2 0 0 2 0
0 0 0 0 0 2 0 2 0 0 0 2 2 0 2 0 2 2 0 0 2 2 2 2 0 2 0 2 0 2 2 2 0 2 0 2 2 0 0 0 2 2 2 0 0 2 0 0 0 0 0 2 0 2 2 2 0 2
generates a code of length 58 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.
Homogenous weight enumerator: w(x)=1x^0+275x^52+44x^53+180x^55+280x^56+288x^57+296x^59+221x^60+172x^61+36x^63+179x^64+8x^65+55x^68+12x^72+1x^92
The gray image is a code over GF(2) with n=232, k=11 and d=104.
This code was found by Heurico 1.16 in 21.3 seconds.