The generator matrix

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

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+321x^30+1192x^31+2363x^32+3906x^33+5421x^34+6242x^35+5820x^36+3942x^37+2067x^38+964x^39+316x^40+134x^41+63x^42+2x^43+12x^44+2x^45

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.