The generator matrix

 1  0  1  1  1 X^2+X+2  X  1  1 X^2+2  1  1  1  1  2 X^2+X+2  1  1  1 X^2+X  1  1  1 X^2+X  1  1  1  1  1  1
 0  1 X+1 X^2+X X^2+3  1  1  2 X^2+1  1 X^2+X+1 X^2+X+2 X^2+2 X+1  1  1  0  1 X^2+X+3  1  X X^2+1  2  1 X^2+3 X^2+X+1 X^2+1  1  3 X+1
 0  0 X^2  0 X^2+2 X^2 X^2+2 X^2  2  0 X^2+2 X^2  2  2 X^2 X^2+2  0 X^2  2  0 X^2  0 X^2+2  2 X^2+2 X^2+2 X^2+2 X^2+2  0  0
 0  0  0  2  0  0  2  0  2  2  2  2  2  0  0  2  0  2  2  2  0  0  2  0  0  0  2  0  0  0
 0  0  0  0  2  0  2  2  0  2  2  0  2  2  2  0  2  2  2  2  2  0  0  0  0  2  2  0  2  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+110x^26+208x^27+538x^28+816x^29+786x^30+816x^31+503x^32+208x^33+86x^34+12x^36+6x^38+4x^42+2x^44

The gray image is a code over GF(2) with n=240, k=12 and d=104.
This code was found by Heurico 1.16 in 0.093 seconds.