The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1 X^3+X^2  1  X  1  1  1 X^2+X X^3  1  1  1  1 X^3+X  1 X^2  1  1  0  1  1 X^3+X  1  1  1  1  1 X^2+X  0 X^3+X^2 X^3+X  1  1  1  1  1 X^3+X^2 X^2+X  1  1  1  X  1  1  1  1  1  1  1  1  1 X^3+X^2 X^2+X  X  1  1  1  1  1 X^3+X  1  X  1 X^3 X^3+X
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3+X^2+1 X^3+X^2  1  X  1 X^3+1 X+1  0  1  1 X^3+X^2+X X^2+X+1  1 X^3+X^2  1 X^3+X^2+X+1  1  X X+1  1 X^2+X X^2+1  1 X^2+X X^3 X^2 X^2+X+1 X^2+1  1  1  1  1 X^3 X^2 X^3+X+1  1 X^3+X  1  1 X^2+X+1 X^3+X  1 X^3+X^2+X X^3 X^2+1 X^3+X^2+X+1  X X^3+X^2+X X^3  X X^3 X^2+X  1  1  X X^3 X^3+X^2+1 X+1 X^3+X^2+X+1 X^2  1  0  1 X+1  1  1
 0  0 X^2  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^2  0 X^2 X^3+X^2 X^2 X^3  0 X^3 X^3+X^2 X^3 X^2 X^2  0  0 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^2 X^3  0  0 X^2  0 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2 X^3 X^3+X^2  0 X^2 X^3  0 X^3 X^3  0 X^3+X^2 X^2  0 X^2 X^3  0 X^2 X^3
 0  0  0 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^2 X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3  0 X^3 X^3+X^2 X^2 X^2 X^2  0 X^3  0 X^2 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^3  0 X^2 X^2 X^2 X^3 X^3+X^2 X^3 X^2 X^2  0  0  0 X^2  0 X^3+X^2  0 X^3 X^2 X^3+X^2 X^3+X^2  0  0 X^3 X^3+X^2  0 X^3+X^2

generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+489x^68+360x^69+540x^70+448x^71+569x^72+368x^73+536x^74+320x^75+370x^76+40x^77+12x^78+23x^80+11x^84+5x^88+2x^92+2x^96

The gray image is a linear code over GF(2) with n=576, k=12 and d=272.
This code was found by Heurico 1.16 in 27.2 seconds.