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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+100x^67+185x^68+270x^69+350x^70+408x^71+498x^72+536x^73+494x^74+396x^75+338x^76+230x^77+162x^78+74x^79+9x^80+20x^81+2x^82+8x^83+4x^84+2x^87+3x^88+4x^91+1x^92+1x^112

The gray image is a linear code over GF(2) with n=584, k=12 and d=268.
This code was found by Heurico 1.16 in 1 seconds.