The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+322x^32+728x^33+812x^34+804x^35+493x^36+448x^37+246x^38+116x^39+95x^40+16x^41+14x^42+1x^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.