The generator matrix
1 0 1 1 1 2 1 1 X X 1 1 2 1 1 X+2 1 1 0 1 1 X 1 1 X+2 X+2 X X X 2 2 2 X 2 X X X+2 2 0 1 1 1 1 2 1 0 1 X+2 X 2 X+2 1 1 1 0 1 1 1
0 1 1 0 X+1 1 X+3 0 1 1 2 1 1 X X+1 1 X+2 X+1 1 X 1 1 X 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X+1 X X 1 3 1 X 1 1 1 1 3 3 X+3 1 X+2 3 0
0 0 X 0 0 0 0 X X+2 X+2 X X 2 X+2 X+2 X+2 X+2 X+2 2 2 2 X+2 2 2 X 0 2 0 0 X X+2 X+2 2 X 2 2 X+2 X X+2 X X+2 2 X 0 X+2 0 0 X X+2 2 2 2 0 X+2 2 2 X+2 2
0 0 0 X 2 X+2 X+2 X 2 X+2 2 X+2 X+2 0 X X X+2 2 2 X+2 X 0 2 0 X 0 0 X X+2 0 2 X 2 X+2 X+2 X 0 X 0 X+2 X+2 X X+2 2 X+2 X+2 X+2 0 X X 0 2 X X+2 X 0 2 0
generates a code of length 58 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+210x^54+226x^56+184x^58+216x^60+160x^62+3x^64+16x^66+6x^70+2x^88
The gray image is a code over GF(2) with n=232, k=10 and d=108.
This code was found by Heurico 1.16 in 19.3 seconds.