The generator matrix

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

generates a code of length 76 over Z2[X]/(X^4) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+128x^71+309x^72+414x^73+554x^74+496x^75+530x^76+382x^77+517x^78+316x^79+168x^80+152x^81+72x^82+18x^83+14x^84+10x^85+3x^86+1x^88+1x^90+2x^91+4x^94+1x^96+2x^97+1x^98

The gray image is a linear code over GF(2) with n=608, k=12 and d=284.
This code was found by Heurico 1.16 in 0.687 seconds.