The generator matrix

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

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+68x^53+154x^54+258x^55+309x^56+378x^57+402x^58+364x^59+369x^60+358x^61+362x^62+342x^63+309x^64+160x^65+88x^66+62x^67+26x^68+20x^69+16x^70+24x^71+7x^72+6x^73+2x^74+6x^75+1x^76+2x^77+2x^80

The gray image is a linear code over GF(2) with n=240, k=12 and d=106.
This code was found by Heurico 1.16 in 0.858 seconds.