The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X 2X+2  1  1  1  X  1  1  1
 0  2  0  2  0  2  0 2X+2 2X  2  0  2  2  0  2 2X 2X+2  0 2X  2  2 2X+2 2X  0 2X  0  0 2X  2  2 2X+2  2 2X+2  2  2
 0  0 2X  0  0  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X  0 2X 2X
 0  0  0 2X  0  0  0 2X  0  0  0 2X  0  0 2X  0  0 2X 2X  0 2X 2X 2X  0  0 2X 2X 2X 2X 2X  0  0 2X 2X  0
 0  0  0  0 2X  0  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0
 0  0  0  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X  0 2X  0 2X  0  0 2X
 0  0  0  0  0  0 2X  0 2X  0 2X  0  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X  0  0  0 2X 2X  0  0  0 2X 2X 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+53x^30+56x^31+105x^32+64x^33+234x^34+1048x^35+238x^36+64x^37+86x^38+40x^39+34x^40+6x^42+8x^43+2x^44+4x^46+4x^48+1x^62

The gray image is a code over GF(2) with n=280, k=11 and d=120.
This code was found by Heurico 1.16 in 111 seconds.