The generator matrix

 1  0  0  1  1  1  2  1  1 X^2+2 X^2+X X^2  1  1  1  1  1  X X+2  1  0  X X^2+X  1  1  X  1  1  1  1 X^2+2  1 X^2+X+2  0  1
 0  1  0  2 X^2+1 X^2+3  1 X^2 X^2+2 X^2+X  1  1 X^2+X+1  3 X+1 X^2+X+2  1  1  1 X^2+X+3  1 X^2  1 X+2 X^2+3 X+2  X X^2+X+1  2 X^2+X+2  1 X^2+2  1  1 X^2+2
 0  0  1 X+3 X+1  2 X^2+X+1  X  3  1 X^2+X+2  1 X^2+X+3 X+2 X^2+X X^2+2 X^2+3 X+3  1  2 X^2+X+2  1  2 X^2+1 X^2  1 X^2+X+1 X^2+3  3 X+2 X+1 X+3 X+1  1 X^2+X+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+314x^32+810x^33+747x^34+744x^35+466x^36+522x^37+279x^38+108x^39+74x^40+24x^41+6x^42+1x^44

The gray image is a code over GF(2) with n=280, k=12 and d=128.
This code was found by Heurico 1.16 in 0.078 seconds.