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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+344x^71+404x^72+272x^73+263x^74+250x^75+132x^76+160x^77+96x^78+50x^79+29x^80+36x^81+8x^83+1x^86+1x^96+1x^100

The gray image is a linear code over GF(2) with n=592, k=11 and d=284.
This code was found by Heurico 1.16 in 4.81 seconds.