The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+142x^27+310x^28+402x^29+426x^30+352x^31+260x^32+98x^33+20x^34+16x^35+4x^36+12x^37+2x^38+2x^39+1x^40

The gray image is a code over GF(2) with n=240, k=11 and d=108.
This code was found by Heurico 1.16 in 0.016 seconds.