The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+92x^24+718x^25+2333x^26+6774x^27+15481x^28+30766x^29+47365x^30+54872x^31+47480x^32+31150x^33+15423x^34+6656x^35+2171x^36+594x^37+191x^38+48x^39+23x^40+4x^41+2x^43

The gray image is a code over GF(2) with n=248, k=18 and d=96.
This code was found by Heurico 1.16 in 205 seconds.