The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1 X^2 X^2  1  1  X  X  1  X  1  1  X  X  1  X
 0  X  0  X  0 X^3 X^3+X  X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X  0 X^3+X^2  X X^3+X^2+X  X  0 X^3 X^3+X X^2  0 X^2+X X^3+X X^2 X^3+X^2+X X^2+X  0 X^2  X X^3+X  0 X^3  X  0 X^3+X^2+X  X X^2 X^3+X^2 X^3  X X^3+X^2+X X^3 X^3+X X^2 X^3+X^2 X^2+X X^3+X^2+X X^3+X^2 X^2 X^3+X^2 X^2  0 X^3 X^2+X X^2+X X^3+X^2+X X^2+X  X  X X^2+X X^3+X^2+X X^2 X^3+X^2 X^3+X X^2  X X^3+X X^2+X X^2+X X^3 X^3+X
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^2 X^2 X^3+X^2+X  X  0 X^3 X^3+X^2+X X^3+X X^2  0 X^3+X  X X^2 X^3+X^2+X  X X^3+X^2 X^3+X^2 X^2 X^2+X X^3+X^2+X X^3 X^2+X X^3+X X^3 X^3 X^3 X^3+X X^2  X X^2 X^2 X^3+X X^3+X^2 X^3+X^2+X  X  X X^3 X^2+X X^2 X^2 X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^3 X^3+X^2+X X^3+X^2+X X^2+X X^2+X X^2+X X^3+X^2+X  X  X  X X^3+X  0  0  X X^2+X X^3 X^3+X^2+X X^3 X^3 X^3  0  X X^3+X^2+X
 0  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0  0  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 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+244x^71+359x^72+296x^73+373x^74+436x^75+739x^76+420x^77+371x^78+292x^79+300x^80+204x^81+19x^82+16x^83+8x^85+5x^86+4x^87+8x^88+1x^132

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 55.5 seconds.