The generator matrix

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

generates a code of length 32 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+268x^30+128x^31+342x^32+32x^33+172x^34+32x^35+39x^36+8x^38+1x^40+1x^44

The gray image is a code over GF(2) with n=256, k=10 and d=120.
This code was found by Heurico 1.16 in 18.6 seconds.