The generator matrix

 1  0  1  1  1 X^2+X  1  1  X  1  1 X^2  1  1 X^2+X  1  1  1 X^2  1  1  0 X^2+X  1  1  1  1  1  1  1  0  1 X^2+X  X  1  1 X^2+X  0  1  0 X^2  1  1  1  1  X  1 X^2+X X^2+X X^2+X  0  1  1  1  0  1  1  1  1  0
 0  1  1 X^2+X X^2+X+1  1 X^2 X+1  1  X X^2+1  1 X^2+X  1  1  0 X+1 X^2+1  1 X^2  X  1  1 X^2+X+1  0  X  X  X  0  0  1  X  1  1 X^2  1  1  1 X+1  1  1  0 X^2+X  X  X  1 X^2  1  1  1  1 X^2+X+1  1 X^2  1 X^2+X+1 X^2+X+1  1 X^2  X
 0  0  X  0 X^2+X  0  X X^2  X  X X^2  X  0  X  0 X^2  0 X^2  X  X X^2+X  X X^2 X^2+X  X  X  0  0  0 X^2+X X^2 X^2+X X^2+X  X X^2 X^2  0 X^2+X  X  0  0  0  0 X^2+X X^2  0 X^2 X^2+X  X  0 X^2 X^2+X  X  0 X^2  X  X  0  X X^2
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+96x^54+80x^55+238x^56+152x^57+239x^58+152x^59+196x^60+160x^61+215x^62+144x^63+180x^64+72x^65+69x^66+8x^67+11x^68+21x^70+8x^72+5x^76+1x^88

The gray image is a linear code over GF(2) with n=240, k=11 and d=108.
This code was found by Heurico 1.16 in 0.306 seconds.