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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+44x^64+40x^65+89x^66+122x^67+159x^68+242x^69+256x^70+328x^71+321x^72+330x^73+377x^74+338x^75+330x^76+280x^77+196x^78+172x^79+115x^80+104x^81+69x^82+50x^83+37x^84+22x^85+24x^86+12x^87+13x^88+6x^89+9x^90+2x^91+2x^92+3x^94+2x^96+1x^110

The gray image is a linear code over GF(2) with n=296, k=12 and d=128.
This code was found by Heurico 1.16 in 1.69 seconds.