The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X+2  1  1  1  1  1 2X+2  1
 0  2  0  2  0  2  0  2  0  2 2X 2X+2  0  2 2X 2X+2  0  2 2X  2 2X+2 2X+2  0 2X  0  0 2X 2X 2X  2  2 2X+2 2X+2 2X  0
 0  0 2X  0  0  0 2X  0  0  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0
 0  0  0 2X  0  0  0 2X  0  0  0  0 2X 2X 2X  0 2X 2X 2X 2X  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0 2X  0  0
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X 2X 2X 2X  0  0
 0  0  0  0  0 2X  0 2X 2X 2X 2X  0  0  0  0  0  0 2X  0 2X 2X  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X  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+51x^32+224x^33+43x^34+512x^35+128x^37+12x^40+32x^41+20x^42+1x^66

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 0.031 seconds.