The generator matrix
1 0 1 1 1 X 1 1 1 1 0 X X X 0 1 1 1
0 1 X+1 X 1 1 0 X X+1 1 1 1 0 X X 0 X+1 X
generates a code of length 18 over Z2[X]/(X^2) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+3x^18+8x^19+3x^20+1x^22
The gray image is a linear code over GF(2) with n=36, k=4 and d=18.
As d=18 is an upper bound for linear (36,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000627 seconds.