The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X X^2 X^2+X+2  1  1  1  1 X^2+X+2  1 X^2  1  X  1  1  1  1  1  1 X^2+2  1  1  X X+2  1
 0  1  1 X^2 X+1  1  X  3  1 X+2 X^2+X+1  1  1  1 X^2 X^2+3 X+2 X+1  1  2  1  X  1  3 X^2+X+3  0 X^2+X+1 X^2+X+2 X^2+1  1  2 X^2+X+2  X  1 X^2+X+2
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2  0  X  0 X^2 X^2+2 X^2+X+2 X^2+2 X^2+X+2 X^2  X X^2+2 X+2 X^2+2 X^2+X+2 X^2+X X^2+X X^2+X X^2+2 X^2 X^2+X+2 X^2+X+2 X+2  0  2  0  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+119x^32+466x^33+298x^34+348x^35+295x^36+390x^37+72x^38+40x^39+4x^41+1x^42+8x^44+5x^46+1x^48

The gray image is a code over GF(2) with n=280, k=11 and d=128.
This code was found by Heurico 1.16 in 0.047 seconds.