The generator matrix

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

generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+70x^59+137x^60+178x^61+177x^62+236x^63+269x^64+270x^65+238x^66+218x^67+273x^68+186x^69+219x^70+240x^71+210x^72+200x^73+163x^74+156x^75+192x^76+150x^77+66x^78+82x^79+59x^80+34x^81+27x^82+20x^83+10x^84+6x^85+6x^86+2x^87+1x^88

The gray image is a linear code over GF(2) with n=138, k=12 and d=59.
This code was found by Heurico 1.16 in 2.58 seconds.