The generator matrix

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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+33x^60+52x^61+156x^62+130x^63+246x^64+190x^65+384x^66+266x^67+468x^68+278x^69+465x^70+270x^71+409x^72+170x^73+241x^74+94x^75+108x^76+78x^77+19x^78+8x^79+7x^80+5x^82+6x^84+5x^86+1x^88+1x^90+1x^92+3x^94+1x^98

The gray image is a linear code over GF(2) with n=276, k=12 and d=120.
This code was found by Heurico 1.16 in 1.1 seconds.