The generator matrix

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

generates a code of length 76 over Z2[X]/(X^4) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+100x^72+256x^73+367x^74+266x^75+226x^76+188x^77+243x^78+212x^79+118x^80+36x^81+28x^82+2x^84+2x^91+1x^94+1x^96+1x^106

The gray image is a linear code over GF(2) with n=608, k=11 and d=288.
This code was found by Heurico 1.16 in 0.5 seconds.