The generator matrix

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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+368x^70+488x^71+649x^72+440x^73+494x^74+424x^75+382x^76+360x^77+304x^78+80x^79+53x^80+14x^82+32x^84+4x^86+1x^92+1x^96+1x^100

The gray image is a linear code over GF(2) with n=592, k=12 and d=280.
This code was found by Heurico 1.16 in 0.625 seconds.