The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  1  1  1  1  1  1  1  X  X  1  1  X  X
 0 2X  0  0  0  0  0 2X  0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0  0  0 2X  0  0 2X  0 2X 2X 2X  0 2X  0 2X
 0  0 2X  0  0  0  0 2X  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X 2X 2X
 0  0  0 2X  0  0  0 2X  0 2X 2X  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X
 0  0  0  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X  0 2X  0 2X 2X 2X 2X  0  0 2X  0  0  0  0  0  0 2X 2X 2X 2X
 0  0  0  0  0 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0
 0  0  0  0  0  0 2X 2X 2X  0 2X  0  0  0 2X 2X 2X  0 2X  0 2X 2X 2X 2X  0  0  0  0 2X  0  0  0 2X 2X  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+34x^30+64x^32+38x^34+768x^35+32x^36+50x^38+27x^40+2x^42+4x^46+3x^48+1x^56

The gray image is a code over GF(2) with n=280, k=10 and d=120.
This code was found by Heurico 1.16 in 1.47 seconds.