The generator matrix

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

generates a code of length 70 over Z2[X]/(X^4) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+126x^61+955x^62+2374x^63+4854x^64+8830x^65+14043x^66+20724x^67+27752x^68+33270x^69+35623x^70+33614x^71+28376x^72+21538x^73+13991x^74+8062x^75+4302x^76+2132x^77+950x^78+300x^79+177x^80+80x^81+34x^82+14x^83+10x^84+8x^85+4x^86

The gray image is a linear code over GF(2) with n=560, k=18 and d=244.
This code was found by Heurico 1.16 in 605 seconds.