The generator matrix

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

generates a code of length 35 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+298x^32+152x^33+456x^34+344x^35+410x^36+136x^37+152x^38+8x^39+71x^40+16x^42+2x^44+1x^48+1x^56

The gray image is a code over GF(2) with n=280, k=11 and d=128.
This code was found by Heurico 1.16 in 24.4 seconds.