The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+115x^30+156x^31+362x^32+420x^33+717x^34+632x^35+684x^36+440x^37+286x^38+140x^39+85x^40+4x^41+29x^42+18x^44+5x^46+2x^48

The gray image is a code over GF(2) with n=280, k=12 and d=120.
This code was found by Heurico 1.16 in 0.203 seconds.