The generator matrix

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

generates a code of length 30 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+174x^26+568x^27+1140x^28+1316x^29+1966x^30+1288x^31+945x^32+496x^33+210x^34+32x^35+40x^36+12x^37+2x^38+2x^40

The gray image is a code over GF(2) with n=240, k=13 and d=104.
This code was found by Heurico 1.16 in 0.25 seconds.