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  1  1  2  1  1  1  2  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X+2 X^2+2 X^2+X+2  0 X+2 X^2+2  2 X^2+X X^2 X+2 X^2+X  0 X+2 X^2+2  0 X^2+X X^2+2 X+2  2  2 X^2 X^2+X+2  X  2  0
 0  0  2  0  0  0  2  0  0  2  2  0  2  2  2  2  2  0  2  0  2  2  2  0  2  0  0  0  0  2  2  0  2  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  0  2  0  0  2  0  2  2  0  0  0  2  0  2  2  2  0  2  2  0  2
 0  0  0  0  2  2  2  2  2  0  2  0  2  0  0  2  0  0  0  2  2  2  2  0  2  2  2  0  0  0  2  0  0  0  2

generates a code of length 35 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+39x^32+296x^33+39x^34+368x^35+20x^36+200x^37+12x^38+4x^40+32x^41+12x^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 0.047 seconds.