The generator matrix

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

generates a code of length 69 over Z2[X]/(X^4) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+212x^61+1023x^62+2454x^63+4700x^64+7412x^65+10500x^66+13786x^67+17045x^68+17046x^69+16659x^70+14192x^71+11153x^72+7036x^73+3992x^74+2070x^75+1003x^76+474x^77+189x^78+70x^79+26x^80+12x^81+4x^82+4x^83+8x^84+1x^86

The gray image is a linear code over GF(2) with n=552, k=17 and d=244.
This code was found by Heurico 1.16 in 156 seconds.