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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+91x^66+149x^68+24x^69+136x^70+96x^71+288x^72+152x^73+297x^74+128x^75+212x^76+72x^77+170x^78+32x^79+73x^80+8x^81+53x^82+33x^84+12x^86+6x^88+7x^90+5x^92+2x^94+1x^124

The gray image is a linear code over GF(2) with n=296, k=11 and d=132.
This code was found by Heurico 1.16 in 0.916 seconds.