The generator matrix

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

generates a code of length 35 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+33x^30+136x^31+159x^32+768x^33+329x^34+1264x^35+319x^36+768x^37+144x^38+136x^39+27x^40+3x^42+5x^44+2x^46+1x^48+1x^54

The gray image is a code over GF(2) with n=280, k=12 and d=120.
This code was found by Heurico 1.16 in 0.109 seconds.