The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+46x^30+148x^31+332x^32+444x^33+800x^34+690x^35+793x^36+330x^37+219x^38+144x^39+103x^40+24x^41+4x^42+10x^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 0.172 seconds.