The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+335x^32+792x^33+702x^34+752x^35+550x^36+488x^37+248x^38+128x^39+72x^40+16x^41+10x^42+2x^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 0.094 seconds.