The generator matrix

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

generates a code of length 30 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+364x^25+1961x^26+4232x^27+7721x^28+11744x^29+13574x^30+11610x^31+8017x^32+4124x^33+1613x^34+396x^35+133x^36+40x^37+4x^38+2x^39

The gray image is a code over GF(2) with n=240, k=16 and d=100.
This code was found by Heurico 1.16 in 14.5 seconds.