The generator matrix

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

generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+508x^69+120x^70+384x^71+28x^72+432x^73+96x^74+448x^75+12x^77+8x^78+8x^81+3x^96

The gray image is a linear code over GF(2) with n=576, k=11 and d=276.
This code was found by Heurico 1.16 in 102 seconds.