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

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+21x^26+172x^27+258x^28+392x^29+365x^30+448x^31+211x^32+120x^33+26x^34+20x^35+10x^36+3x^38+1x^50

The gray image is a code over GF(2) with n=240, k=11 and d=104.
This code was found by Heurico 1.16 in 0.032 seconds.