The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  2  1  1  1  1  1 X^2+2  1  1  X  1  1  2  1  2  X  1
 0  X  0  X  0  2 X^2+X  X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X+2 X^2+2 X^2+X X+2 X^2  2 X^2+X  X X^2 X^2+X+2  2 X^2+X X^2 X^2+X+2  0  0  X  X  X X^2+X  0
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2 X^2+2  2  0 X^2+2  X X^2+X X+2 X+2  0 X^2+X  X  X X^2+X+2  2 X+2 X^2+2  X X+2  2 X^2  0 X^2+X  X  0 X^2+2 X^2+X  2
 0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  0  2  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  2  0  2
 0  0  0  0  2  2  0  0  0  2  2  2  0  2  0  2  0  0  0  2  2  0  2  0  2  2  0  0  2  2  0  2  2  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+52x^30+132x^31+343x^32+460x^33+779x^34+690x^35+783x^36+338x^37+239x^38+136x^39+86x^40+32x^41+15x^42+2x^43+3x^44+2x^45+2x^46+1x^54

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 0.156 seconds.