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  1  1  1  1  1  1  1  0  1  X  X  1  1  1 X^2  1  X  1  X  X  1  1  X  1  1 X^2  1  1  1  1  1  1  1  0  X  0  X  X  X  1  X  1  1
 0  X  0  0  0  0  0  0 X^2  X X^2+X X^2+X  X  X  X  X X^2  0 X^2 X^2  X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2  0  0 X^2  X  0  0 X^2+X  X X^2+X X^2+X X^2 X^2+X X^2  X X^2 X^2+X  0 X^2  X X^2+X  X X^2  0  X X^2  0 X^2+X  0 X^2+X  X X^2 X^2  0  0  X X^2+X  0  X X^2 X^2+X X^2
 0  0  X  0  0  0  X X^2+X X^2+X  X  X X^2  X  X X^2+X  0 X^2 X^2 X^2+X  X X^2  0  X X^2  X X^2  0  X  0  X  0 X^2+X X^2+X X^2  X  X X^2+X  0  X X^2+X X^2  X  X X^2 X^2  0  0 X^2+X X^2  0 X^2+X  X X^2  X  X  0 X^2+X X^2+X  0  X  X  X X^2 X^2 X^2+X  0  0  X  0
 0  0  0  X  0  X  X  X  0 X^2  0  X X^2+X X^2+X X^2  0 X^2+X X^2 X^2+X  0 X^2+X X^2 X^2 X^2+X  X  0 X^2+X X^2  X X^2+X  0 X^2+X X^2+X  X X^2  X  X  0  0 X^2  X X^2+X X^2 X^2 X^2+X  X  X  X X^2+X X^2+X  0  X  X X^2 X^2  0  0 X^2+X  X  0  0 X^2  0 X^2+X  0 X^2+X  X  X X^2
 0  0  0  0  X  X X^2 X^2+X  X X^2  X  0  X  0  X  0 X^2  0  X X^2+X X^2+X  X X^2 X^2  X X^2+X X^2+X X^2 X^2+X X^2 X^2+X  0 X^2 X^2  0 X^2+X X^2  X X^2  X  X X^2+X  0 X^2  X X^2+X  X X^2+X  0 X^2+X X^2  X X^2 X^2 X^2+X  0  0 X^2 X^2  X  X  0  X  0  0 X^2+X  0 X^2 X^2+X
 0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  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 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 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+52x^60+84x^61+111x^62+152x^63+311x^64+138x^65+461x^66+126x^67+632x^68+106x^69+625x^70+112x^71+451x^72+92x^73+258x^74+76x^75+67x^76+64x^77+50x^78+40x^79+17x^80+26x^81+28x^82+6x^83+5x^84+2x^85+2x^86+1x^106

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 1.43 seconds.