The generator matrix

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

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+77x^54+208x^55+115x^56+240x^57+48x^58+344x^59+40x^60+256x^61+84x^62+320x^63+83x^64+144x^65+32x^66+24x^67+8x^68+11x^70+7x^72+2x^78+2x^80+2x^86

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 1.22 seconds.