The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+112x^30+636x^31+1233x^32+2064x^33+2946x^34+2694x^35+2735x^36+2098x^37+1016x^38+490x^39+244x^40+76x^41+30x^42+2x^43+3x^44+2x^45+2x^47

The gray image is a code over GF(2) with n=280, k=14 and d=120.
This code was found by Heurico 1.16 in 1.25 seconds.