The generator matrix

 1  0  0  1  1  1  0 X^3+X^2 X^3+X^2 X^3+X^2  1  1  1  1 X^2+X  1  1 X^3+X  1  X  1 X^3+X  1  1  X  X  1  1 X^3+X^2+X  1  1 X^3+X^2 X^2 X^2 X^2  1 X^3+X^2+X  1  1  1  1 X^3+X X^2+X  1 X^3+X^2  1 X^3+X^2  1 X^2  1  1  1  1  1  1  1 X^3+X^2+X  1 X^3+X^2+X  1 X^3+X^2 X^2  1 X^2+X  1 X^3  1 X^3+X^2+X  1  X  0 X^2+X  1
 0  1  0  0 X^2+1 X^3+X^2+1  1  X  1  1 X^2+1 X^2+1 X^3+X^2 X^2 X^2 X^2+X+1 X^2+X  1 X^3+X  1 X^3+X+1 X^2+X X^3+X X^3+X^2+X  1  1 X+1 X^3+X+1  1 X^3+X^2+1 X^3+X^2+X+1  1  1  1  1  X  X  X X^3+X^2+1  1 X^2  1  1 X^3+X^2 X^3+X^2 X^2+X+1  1 X^3+1 X^3+X^2+X X^3+X+1 X^2+X+1 X+1 X^2+X X^3+1 X^2+X X^2+X+1 X^3+X^2 X+1  1 X^3+1  1  X X^3+X^2  1  X X^3 X^3+X^2+X  1 X^3+X^2+X+1  1  1  1  0
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X X^3+1 X^3+1 X^3+X^2+X  X X^3+X^2+1  1 X^2+X  X X^3+X^2 X^3+X+1 X^2+1  1  1  1  0 X^3+X^2+X+1 X^3+X X^3 X^2+1 X^3 X^3+X^2 X^3+X+1  0  X X^2+X+1 X^3+1 X^3+X+1  1  0  X X^2+1 X^3+X^2+X+1  X  1 X^3+1  1 X^3+X^2 X^3 X+1  1 X+1 X^3+X^2+X X+1  1 X^2  1  0  1 X+1 X^3+X^2+1 X^3+1 X^3+1  1 X^3+X X^2+X+1 X^3+X  1 X^3 X+1 X^2+1 X^2+X X^3+1 X^3+X^2+X+1  0
 0  0  0 X^2 X^2  0 X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2  0 X^2 X^2 X^3+X^2  0 X^3 X^2  0  0 X^2 X^3 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3+X^2  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^3 X^2  0 X^3+X^2 X^2 X^2 X^2  0  0 X^3+X^2  0 X^3 X^2 X^3 X^3+X^2  0  0  0 X^3 X^2 X^3+X^2 X^3 X^3 X^3  0 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2  0 X^2 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+120x^67+657x^68+948x^69+2089x^70+1554x^71+2331x^72+1790x^73+2109x^74+1404x^75+1461x^76+648x^77+689x^78+218x^79+205x^80+66x^81+36x^82+32x^83+16x^84+2x^85+4x^86+1x^88+1x^90+2x^93

The gray image is a linear code over GF(2) with n=584, k=14 and d=268.
This code was found by Heurico 1.16 in 7.31 seconds.