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

generates a code of length 75 over Z2[X]/(X^4) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+98x^69+689x^70+1150x^71+1715x^72+1874x^73+2150x^74+2070x^75+1716x^76+1534x^77+1284x^78+820x^79+638x^80+288x^81+172x^82+86x^83+49x^84+12x^85+23x^86+2x^87+6x^88+2x^89+2x^90+3x^92

The gray image is a linear code over GF(2) with n=600, k=14 and d=276.
This code was found by Heurico 1.16 in 4.89 seconds.