The generator matrix

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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+102x^69+670x^70+674x^71+698x^72+438x^73+502x^74+302x^75+250x^76+104x^77+134x^78+72x^79+89x^80+32x^81+21x^82+4x^85+2x^88+1x^90

The gray image is a linear code over GF(2) with n=584, k=12 and d=276.
This code was found by Heurico 1.16 in 0.297 seconds.