The generator matrix

 1  0  0  1  1  1  2  0 2X  2  1  1 3X+2  1  1 3X  1  1  1  1 X+2  1 X+2  1  1  0 3X  1  1  1  1 3X  0  1  1
 0  1  0  0 2X+3 2X+3  1 X+2  1  1 X+2 3X+1  1 3X+3 X+2 2X 3X+2 3X+3 X+1 2X  1 2X+1 X+2  X  2 3X 3X+2 X+1 2X+2  0  3  2  1 2X+1  0
 0  0  1 X+1 X+3  2 X+3  1 3X+2  1  0 2X+2 2X X+1 3X+1  1  X X+2  3 2X+3 X+2 2X+1  1  1 X+2  1  1 3X+1 X+2 X+3 3X+2  1 2X+2 3X+2 2X+2
 0  0  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0 2X  0  0  0 2X 2X 2X 2X  0 2X 2X 2X  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+168x^31+766x^32+1136x^33+1351x^34+1636x^35+1273x^36+890x^37+575x^38+232x^39+117x^40+20x^41+9x^42+12x^43+3x^44+2x^45+1x^46

The gray image is a code over GF(2) with n=280, k=13 and d=124.
This code was found by Heurico 1.16 in 0.312 seconds.