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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+51x^48+80x^49+192x^50+224x^51+321x^52+376x^53+538x^54+758x^55+938x^56+1140x^57+1325x^58+1454x^59+1566x^60+1578x^61+1303x^62+1180x^63+855x^64+760x^65+542x^66+396x^67+278x^68+140x^69+148x^70+78x^71+74x^72+20x^73+37x^74+6x^75+10x^76+2x^77+11x^78+1x^80+1x^84

The gray image is a linear code over GF(2) with n=240, k=14 and d=96.
This code was found by Heurico 1.16 in 17.9 seconds.