The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  X  1  1  1  1  1  1  X  1  1  1  X  2  1 2X+2  1  1  X
 0  X  0 3X+2 2X+2 X+2  2  X  0 3X  2 3X+2 2X  X X+2 2X+2  X X+2  2 2X 3X  0 X+2  0 3X+2 X+2 2X  0  X  X  2 2X+2  0 3X  X
 0  0  2  0 2X+2 2X+2 2X 2X+2  0 2X  0  0 2X+2 2X 2X+2 2X+2  2  2 2X+2 2X+2  0  0 2X  2 2X  2 2X 2X+2  2 2X  0  2  2  0  2
 0  0  0 2X  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0 2X 2X  0  0  0  0  0
 0  0  0  0 2X  0  0 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X  0  0  0  0 2X 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+88x^31+200x^32+164x^33+432x^34+280x^35+515x^36+144x^37+80x^38+80x^39+42x^40+12x^41+9x^44+1x^56

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 31.6 seconds.