The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  X  1  X  2 X^2  X  1 X^2+2  1  X  1  1
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0 X^2+X X^2+2 X+2  2  X  X X^2+2 X^2+X+2 X^2+X X^2+X+2  X  X  X  X X^2+X  2  X  X  0  0  2
 0  0 X^2+2  0 X^2 X^2  2 X^2  0  2  0  0 X^2  2 X^2 X^2 X^2 X^2+2 X^2 X^2 X^2+2 X^2 X^2+2  0 X^2  2 X^2+2 X^2  0 X^2
 0  0  0  2  0  0  2  0  0  2  2  0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  2  0  2  2
 0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  0  2  0  0  0  2  2  0  0  0  2  0  0  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+94x^26+80x^27+347x^28+240x^29+570x^30+240x^31+293x^32+80x^33+66x^34+28x^36+6x^38+2x^40+1x^44

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 0.047 seconds.