The generator matrix

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

generates a code of length 35 over Z2[X]/(X^4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+162x^28+966x^29+3252x^30+7990x^31+17095x^32+31116x^33+43649x^34+52752x^35+44566x^36+31600x^37+17191x^38+7776x^39+2796x^40+852x^41+287x^42+56x^43+20x^44+10x^45+5x^46+2x^47

The gray image is a linear code over GF(2) with n=280, k=18 and d=112.
This code was found by Heurico 1.16 in 239 seconds.