The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+168x^31+313x^32+536x^33+666x^34+776x^35+662x^36+556x^37+224x^38+112x^39+46x^40+24x^41+4x^42+2x^44+4x^45+2x^50

The gray image is a code over GF(2) with n=280, k=12 and d=124.
This code was found by Heurico 1.16 in 18.4 seconds.