The generator matrix

1 0 0 0 0 1 1 1 X 1 1 1 1 0 1 0 X 1 0 1 0 1 1 X 1 1 1 0 X 0
0 1 0 0 0 0 0 0 0 0 0 X X 1 X+1 1 1 1 X 1 0 1 X+1 X 1 X+1 X+1 X X X
0 0 1 0 0 0 1 1 1 0 X 1 X+1 1 1 1 0 X X 1 1 X+1 0 1 1 1 0 1 1 1
0 0 0 1 0 1 0 X+1 1 1 X 1 X X X+1 X+1 1 X 0 0 1 1 X+1 0 1 1 0 X X+1 1
0 0 0 0 1 1 X+1 X 1 X 1 X+1 X 1 0 1 X X 1 1 X 1 1 1 1 0 X+1 1 1 X+1
0 0 0 0 0 X X 0 0 0 0 0 0 0 0 X X X X 0 X 0 X X X 0 0 0 X X

generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+242x^24+240x^26+410x^28+270x^30+441x^32+214x^34+174x^36+42x^38+12x^40+2x^42

The gray image is a linear code over GF(2) with n=60, k=11 and d=24.
As d=24 is an upper bound for linear (60,11,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 11.
This code was found by Heurico 1.10 in 0.156 seconds.