The generator matrix

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

generates a code of length 35 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+40x^30+190x^31+299x^32+548x^33+568x^34+938x^35+591x^36+410x^37+206x^38+154x^39+66x^40+48x^41+17x^42+14x^43+3x^44+2x^45+1x^50

The gray image is a code over GF(2) with n=280, k=12 and d=120.
This code was found by Heurico 1.16 in 0.157 seconds.