The generator matrix

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

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+61x^54+136x^55+167x^56+218x^57+233x^58+212x^59+182x^60+144x^61+178x^62+154x^63+104x^64+110x^65+57x^66+40x^67+20x^68+4x^69+6x^70+2x^71+3x^72+4x^73+6x^74+2x^76+3x^78+1x^80

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 0.3 seconds.