The generator matrix

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

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+154x^31+329x^32+614x^33+574x^34+814x^35+592x^36+558x^37+255x^38+146x^39+34x^40+10x^41+1x^42+2x^43+4x^44+2x^45+1x^46+4x^47+1x^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 0.437 seconds.