The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+24x^66+66x^67+162x^68+248x^69+311x^70+466x^71+502x^72+584x^73+714x^74+674x^75+765x^76+744x^77+694x^78+624x^79+460x^80+388x^81+231x^82+178x^83+131x^84+76x^85+46x^86+30x^87+20x^88+4x^89+22x^90+10x^91+5x^92+4x^93+4x^94+1x^96+1x^98+1x^100+1x^102

The gray image is a linear code over GF(2) with n=304, k=13 and d=132.
This code was found by Heurico 1.16 in 5.18 seconds.