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

generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+114x^66+12x^67+209x^68+68x^69+258x^70+96x^71+250x^72+136x^73+228x^74+140x^75+197x^76+52x^77+108x^78+8x^79+78x^80+44x^82+26x^84+14x^86+6x^88+2x^90+1x^120

The gray image is a linear code over GF(2) with n=292, k=11 and d=132.
This code was found by Heurico 1.16 in 0.524 seconds.