The generator matrix

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

generates a code of length 75 over Z2[X]/(X^4) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+182x^67+1278x^68+3068x^69+5111x^70+7868x^71+10529x^72+13486x^73+15352x^74+17018x^75+15628x^76+14588x^77+10419x^78+7302x^79+4702x^80+2366x^81+1221x^82+564x^83+212x^84+108x^85+56x^86+6x^87+2x^88+4x^91+1x^98

The gray image is a linear code over GF(2) with n=600, k=17 and d=268.
This code was found by Heurico 1.16 in 168 seconds.