The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+176x^31+742x^32+1208x^33+1283x^34+1652x^35+1179x^36+1002x^37+578x^38+206x^39+109x^40+30x^41+11x^42+14x^43+1x^44

The gray image is a code over GF(2) with n=280, k=13 and d=124.
This code was found by Heurico 1.16 in 0.344 seconds.