The generator matrix

 1  0  0  0  0  0  1  1  1  X  0  0  0  0  1  1  1  X  X  0  1  1  1  1  0  1  0  0  1  1  0  0  X  1  1  1  X  1  0  1  1  0  1  X  0  1  1  X  X  X  1  0  1  0  X  1  0  X  1  1
 0  1  0  0  0  0  0  0  0  0  1  X  1  1  0  1  X  X  1  1  X  1  0  1  0  1  1  0  X X+1  1  0  1  0  X X+1  X X+1  1 X+1 X+1  X  0  1  1  1 X+1  X  X  1 X+1  1  0  1  1 X+1  1  1  1  0
 0  0  1  0  0  0  0  0  0  0  X  1  1 X+1 X+1 X+1  1  1  0  X  0  0 X+1 X+1  1  0  1  X  X  1  0  1  X  1 X+1 X+1  0  1  X  0  1  1  X  X  X  X  0  1  1  0  0  0  0  X X+1  X  1  1  1  X
 0  0  0  1  0  0  0  1  1  1 X+1 X+1  1  X  0 X+1  1  1  0  1 X+1  X  1  X  X  1  X  X X+1  X  0  0 X+1  1  X  0  X X+1 X+1  X X+1  1  0  1  0 X+1  1  1  0  0  X  1  0  0 X+1  1 X+1  1  1  1
 0  0  0  0  1  0  1  1  X X+1  1  1  1  0 X+1  0  X  X X+1  X X+1 X+1  1  X X+1  X  1  1  0  1  0  X X+1  1  0  X  X X+1  0  1  0  1  X  X X+1 X+1  0  0  0  X  0  1 X+1  1 X+1  X X+1  0 X+1  0
 0  0  0  0  0  1  1  X X+1  1  0  X  1 X+1  0 X+1  0  1 X+1 X+1  X  0 X+1  X X+1  0  X  0 X+1  1  X  X  0 X+1 X+1  0  1  X X+1  0  0  1 X+1  0  X  0  1  1  0  1 X+1 X+1  X X+1  X  X  0  0  1  X
 0  0  0  0  0  0  X  0  X  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  0  0  X  X  0  0  X  X  X  0  X  0  X  0  X  0  0  X  0  X  0  0  X  X  X  X  0  X  0  X  X  X  0  X  0  X

generates a code of length 60 over Z2[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+64x^49+163x^50+242x^51+305x^52+312x^53+369x^54+434x^55+437x^56+534x^57+517x^58+474x^59+513x^60+542x^61+499x^62+480x^63+484x^64+430x^65+398x^66+254x^67+244x^68+186x^69+96x^70+86x^71+58x^72+44x^73+6x^74+14x^75+5x^76+1x^92

The gray image is a linear code over GF(2) with n=120, k=13 and d=49.
This code was found by Heurico 1.16 in 8.64 seconds.