The generator matrix

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

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+736x^30+2328x^31+4932x^32+7580x^33+10756x^34+12816x^35+10809x^36+8024x^37+4714x^38+1848x^39+729x^40+172x^41+80x^42+7x^44+2x^46+2x^48

The gray image is a code over GF(2) with n=280, k=16 and d=120.
This code was found by Heurico 1.16 in 17.5 seconds.