The generator matrix

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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+186x^66+1248x^67+2918x^68+4920x^69+7790x^70+10330x^71+14219x^72+15576x^73+17096x^74+15932x^75+13752x^76+10342x^77+7786x^78+4498x^79+2479x^80+1168x^81+436x^82+208x^83+116x^84+22x^85+28x^86+8x^87+1x^88+4x^89+2x^90+2x^92+4x^94

The gray image is a linear code over GF(2) with n=592, k=17 and d=264.
This code was found by Heurico 1.16 in 170 seconds.