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

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+111x^32+768x^35+95x^36+48x^40+1x^68

The gray image is a code over GF(2) with n=280, k=10 and d=128.
This code was found by Heurico 1.16 in 0.39 seconds.