The generator matrix

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

generates a code of length 35 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+130x^28+946x^29+3322x^30+8010x^31+17265x^32+30108x^33+45189x^34+51548x^35+45611x^36+31020x^37+17284x^38+7380x^39+3024x^40+974x^41+247x^42+52x^43+17x^44+6x^45+4x^46+2x^47+2x^49+2x^50

The gray image is a code over GF(2) with n=280, k=18 and d=112.
This code was found by Heurico 1.16 in 248 seconds.