The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+48x^53+89x^54+88x^55+173x^56+196x^57+166x^58+220x^59+245x^60+188x^61+154x^62+148x^63+79x^64+72x^65+42x^66+22x^67+33x^68+20x^69+26x^70+16x^71+13x^72+4x^73+2x^74+2x^75+1x^94

The gray image is a linear code over GF(2) with n=240, k=11 and d=106.
This code was found by Heurico 1.16 in 0.352 seconds.