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 X 2 1 1 1 X 1 1 1 1 2 1 1 X 1 1 1 2 1 0 1 1 X 0 1 0 1 0 1 2 X 1
0 X 0 0 0 0 0 2 2 X X+2 X X X X+2 X 0 X+2 2 X 2 X 0 X 2 X+2 2 X+2 X+2 2 X 2 X 0 X+2 X 0 2 0 X+2 X+2 0 0 2 X 0 2 2 X X X 0 0 2 X 2 0
0 0 X 0 0 2 X+2 X X X X X X+2 0 0 0 2 2 X+2 X 2 0 0 X+2 2 0 0 2 0 X+2 0 X X X+2 X+2 X+2 2 X X X X+2 2 X 2 X X X 2 0 0 X 2 X X X X+2 0
0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 0 X X 2 X 2 X+2 0 X+2 0 2 X 2 0 X X X X X 2 X 2 0 2 0 X X+2 2 0 X 0 X+2 0 2 X+2 2 X X+2 X+2 0 X X X 0 X
0 0 0 0 X X 2 X+2 X X+2 2 2 X 2 X+2 X X 2 2 X+2 0 X+2 0 X+2 X+2 2 X X+2 0 X 2 2 2 X 0 0 2 2 X 2 X+2 2 X 2 0 X+2 0 X X+2 X X+2 0 X X X X X
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+68x^50+4x^51+220x^52+60x^53+272x^54+128x^55+234x^56+144x^57+288x^58+116x^59+219x^60+44x^61+102x^62+8x^63+60x^64+8x^65+26x^66+29x^68+10x^70+4x^72+2x^74+1x^88
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 0.317 seconds.