The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1 2X+2  1  1  X  0  X
 0  X  0 3X+2 2X+2 X+2  2  X  0 3X+2 2X 3X  2 3X+2  2  X  0 3X+2  2 2X+2 3X 3X+2 2X 3X 2X+2 3X+2 2X 2X+2 3X  0 2X 2X+2 3X+2  X 3X+2
 0  0  2  0  2 2X+2  0 2X+2 2X 2X 2X+2  2 2X+2  2 2X 2X  0  0  0 2X+2  2 2X+2 2X 2X+2 2X  2 2X+2 2X+2 2X  2  2  2  0 2X  0
 0  0  0 2X 2X  0 2X 2X  0 2X  0 2X 2X  0 2X  0 2X  0  0  0  0 2X 2X  0  0 2X 2X  0 2X 2X 2X  0  0  0  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+121x^32+80x^33+237x^34+224x^35+165x^36+80x^37+74x^38+32x^40+9x^42+1x^60

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 0.047 seconds.