The generator matrix

 1  0  0  0  0  1  1  1  X  1  1  1  1  0  X  1  1  X  1  0  1  0  X  1  1  0  0  1  1  X
 0  1  0  0  0  0  0  0  0  0  0  X  X  1  1 X+1 X+1  1  X  1  X  1  X X+1  1  1  1  X  0  0
 0  0  1  0  0  0  1  1  1  X X+1  X X+1  X  0 X+1  1  1  0  0  0 X+1  1 X+1  0 X+1  0  X X+1  X
 0  0  0  1  0  1  1  X X+1  0  0 X+1  1 X+1  0  X X+1  X  X  0 X+1 X+1 X+1  1  1  1  X  0  X  X
 0  0  0  0  1  1  X X+1  1  1  0  0  1  1  1 X+1  X X+1  X  0  1 X+1  0  X X+1  1 X+1  0  1  0
 0  0  0  0  0  X  0  X  0  0  X  X  0  X  0  0  X  0  X  X  0  X  0  0  X  X  0  X  0  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+296x^24+130x^26+512x^28+168x^30+531x^32+172x^34+176x^36+40x^38+20x^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 1.16 in 2.36 seconds.