The generator matrix

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

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+346x^30+1252x^31+2326x^32+4056x^33+5332x^34+6196x^35+5465x^36+4132x^37+2078x^38+988x^39+402x^40+128x^41+44x^42+12x^43+5x^44+4x^45+1x^48

The gray image is a code over GF(2) with n=280, k=15 and d=120.
This code was found by Heurico 1.16 in 4.66 seconds.