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

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+75x^32+84x^33+222x^34+292x^35+206x^36+60x^37+56x^38+12x^39+13x^40+2x^42+1x^64

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.