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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+325x^70+406x^71+253x^72+294x^73+170x^74+254x^75+186x^76+58x^77+67x^78+12x^79+12x^80+4x^84+4x^86+2x^102

The gray image is a linear code over GF(2) with n=584, k=11 and d=280.
This code was found by Heurico 1.16 in 1.56 seconds.