The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+168x^74+250x^75+262x^76+176x^77+247x^78+182x^79+175x^80+116x^81+99x^82+66x^83+87x^84+46x^85+53x^86+22x^87+24x^88+28x^89+17x^90+8x^91+10x^92+2x^93+8x^94+1x^100

The gray image is a linear code over GF(2) with n=316, k=11 and d=148.
This code was found by Heurico 1.11 in 0.281 seconds.