The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 1 X X X 1 1 1 1 X 2 2 2 X 0 0 0 X X X 1 1 1 X X X X X 2 1 1 1
0 2 0 2 0 0 2 2 0 0 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 0 2 2 0 2 2 0 2 2 0 0 2 2 0 0 2 2 0 0 0 0 2
0 0 2 2 0 2 2 0 0 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 0 2 2 0 2 0 2 2 2 0 0 2 2 0 0 2 2 0 0 0 0 2 2
generates a code of length 54 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+3x^54+22x^55+3x^56+1x^62+2x^63
The gray image is a code over GF(2) with n=216, k=5 and d=108.
This code was found by Heurico 1.16 in 0.0698 seconds.