The generator matrix

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

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+39x^32+336x^33+22x^34+256x^35+24x^36+288x^37+40x^38+16x^41+2x^50

The gray image is a code over GF(2) with n=280, k=10 and d=128.
This code was found by Heurico 1.16 in 0.016 seconds.