The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+159x^32+360x^33+374x^34+320x^35+344x^36+332x^37+124x^38+8x^39+7x^40+4x^41+4x^42+8x^44+2x^46+1x^48

The gray image is a code over GF(2) with n=280, k=11 and d=128.
This code was found by Heurico 1.16 in 0.047 seconds.