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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+56x^66+76x^67+147x^68+186x^69+275x^70+308x^71+381x^72+490x^73+493x^74+648x^75+811x^76+764x^77+610x^78+648x^79+536x^80+422x^81+321x^82+280x^83+209x^84+128x^85+119x^86+76x^87+69x^88+48x^89+33x^90+12x^91+17x^92+10x^93+12x^94+5x^96+1x^114

The gray image is a linear code over GF(2) with n=308, k=13 and d=132.
This code was found by Heurico 1.16 in 7.32 seconds.