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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+46x^60+16x^61+70x^62+60x^63+159x^64+106x^65+297x^66+112x^67+408x^68+140x^69+556x^70+164x^71+603x^72+128x^73+433x^74+124x^75+238x^76+100x^77+125x^78+48x^79+63x^80+22x^81+31x^82+4x^83+8x^84+15x^86+5x^88+7x^90+4x^92+1x^94+1x^96+1x^102

The gray image is a linear code over GF(2) with n=284, k=12 and d=120.
This code was found by Heurico 1.16 in 1.76 seconds.