The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 2X  0  0  0  0  0  0  0  0 2X  0 2X 2X  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X  0  0  0
 0  0 2X  0  0  0  0  0  0  0 2X 2X 2X  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0
 0  0  0 2X  0  0  0 2X 2X 2X  0 2X 2X 2X 2X  0 2X 2X 2X  0 2X 2X  0 2X  0  0  0  0 2X 2X  0  0  0  0  0
 0  0  0  0 2X  0 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X  0 2X 2X  0 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0
 0  0  0  0  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+31x^32+448x^35+31x^38+1x^70

The gray image is a code over GF(2) with n=280, k=9 and d=128.
This code was found by Heurico 1.16 in 0.016 seconds.