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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+127x^68+692x^69+1166x^70+1650x^71+1701x^72+2292x^73+1954x^74+2012x^75+1339x^76+1396x^77+856x^78+578x^79+310x^80+168x^81+66x^82+28x^83+8x^84+12x^85+14x^86+4x^87+8x^90+2x^92

The gray image is a linear code over GF(2) with n=592, k=14 and d=272.
This code was found by Heurico 1.16 in 4.76 seconds.