The generator matrix

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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+138x^64+44x^65+208x^66+172x^67+360x^68+236x^69+362x^70+332x^71+464x^72+292x^73+370x^74+228x^75+335x^76+196x^77+190x^78+36x^79+78x^80+22x^82+13x^84+10x^88+3x^92+5x^96+1x^100

The gray image is a linear code over GF(2) with n=288, k=12 and d=128.
This code was found by Heurico 1.16 in 1.25 seconds.