The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+265x^24+256x^26+304x^28+128x^30+61x^32+8x^36+1x^40

The gray image is a code over GF(2) with n=108, k=10 and d=48.
This code was found by Heurico 1.16 in 9.78 seconds.