The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+300x^26+112x^27+711x^28+552x^29+906x^30+488x^31+564x^32+120x^33+256x^34+8x^35+65x^36+10x^38+3x^40

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 6.55 seconds.