The generator matrix

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

generates a code of length 35 over Z4[X]/(X^3+2,2X) who�s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+102x^31+160x^32+330x^33+230x^34+442x^35+219x^36+314x^37+148x^38+72x^39+1x^40+10x^41+6x^42+6x^43+1x^44+2x^45+2x^47+2x^48

The gray image is a code over GF(2) with n=280, k=11 and d=124.
This code was found by Heurico 1.16 in 0.094 seconds.