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 X 2 X 1 X 1 1 1 X 1 1 X 1 1 1 2 X 1 X 1 1 2 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 X 2 X 0 X+2 2 X X+2 0 X+2 X X X+2 X 0 X+2 X+2 X X 0 2 0 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+2 2 0 2 X X+2 X+2 X+2 2 X+2 0 0 X+2 0 X X X 0 2 2 X X 0 2
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 2 2 X+2 X X X+2 X X+2 0 X 0 2 2 2 0 X X 2 2 0 X+2 X+2 0 X 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 0 0 0 2 0 0 2 0 2 2 0 2 2 2 0 2 2 0 0 0 0 2 2 2 2
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 2 2 0 0 2 0 2 0 0 0 2 2 2 0 0 0 2 0 2 2 2 2 2
generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 50.
Homogenous weight enumerator: w(x)=1x^0+44x^50+102x^51+139x^52+116x^53+139x^54+200x^55+207x^56+218x^57+222x^58+210x^59+113x^60+82x^61+77x^62+46x^63+36x^64+30x^65+25x^66+16x^67+16x^68+2x^69+4x^70+2x^71+1x^90
The gray image is a code over GF(2) with n=228, k=11 and d=100.
This code was found by Heurico 1.16 in 0.349 seconds.