The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  0  1  1 3X+2  X  X  0  X  1  1 3X  1  1  2  1
 0  1 X+1 3X+2 2X+3  1 X+3  2  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  0 X+1  1 3X+2 2X+3  1  0 3X+2  X 2X  2 3X+1  1  2 X+3  1 X+1
 0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X 2X  0  0
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0  0  0 2X 2X  0  0  0 2X 2X 2X 2X  0
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0  0 2X 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0 2X 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+80x^31+169x^32+200x^33+484x^34+224x^35+456x^36+184x^37+152x^38+64x^39+14x^40+16x^41+3x^42+1x^58

The gray image is a code over GF(2) with n=280, k=11 and d=124.
This code was found by Heurico 1.16 in 0.047 seconds.