The generator matrix

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

generates a code of length 35 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+362x^29+1584x^30+4362x^31+8642x^32+15722x^33+22067x^34+25254x^35+22344x^36+16218x^37+8666x^38+3902x^39+1349x^40+430x^41+95x^42+50x^43+14x^44+4x^45+4x^46+2x^48

The gray image is a code over GF(2) with n=280, k=17 and d=116.
This code was found by Heurico 1.16 in 66.1 seconds.