The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2X+2) 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 0.046 seconds.