The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1 2X 2X  1 2X  1  1  1  X  X  X  1  X  1  1  X  1  X  X
 0  X  0 3X+2 2X X+2  0  X  2 3X+2 2X+2 3X 2X+2 2X+2 3X+2  X  X  X  X 2X  X 2X X+2 X+2 X+2 X+2  X  2 3X 2X  0 3X  X X+2 3X
 0  0 2X+2  0 2X 2X+2 2X+2  2  2  2 2X  2  2  0  0 2X 2X 2X+2  0  0 2X+2  2  0 2X+2 2X 2X+2 2X 2X+2 2X+2  0 2X+2 2X 2X 2X+2 2X
 0  0  0 2X+2 2X+2  2 2X+2 2X  0  0 2X+2 2X+2  2 2X 2X 2X  2 2X 2X+2  2  2 2X  0 2X+2  0  2 2X+2 2X+2 2X 2X 2X 2X 2X+2  0  0

generates a code of length 35 over Z4[X]/(X^2+2) 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 0.078 seconds.