The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+379x^30+1062x^31+2764x^32+3600x^33+5689x^34+5774x^35+5849x^36+3726x^37+2497x^38+850x^39+423x^40+76x^41+55x^42+10x^43+3x^44+6x^45+4x^46

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 4.89 seconds.