The generator matrix

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

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+527x^72+368x^73+612x^74+272x^75+600x^76+288x^77+640x^78+336x^79+345x^80+16x^81+60x^82+14x^84+5x^88+10x^92+2x^104

The gray image is a linear code over GF(2) with n=608, k=12 and d=288.
This code was found by Heurico 1.16 in 71.6 seconds.