The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^24+16x^26+124x^28+320x^30+1024x^31+381x^32+48x^34+64x^36+20x^40+4x^44+2x^48

The gray image is a code over GF(2) with n=248, k=11 and d=96.
This code was found by Heurico 1.16 in 0.062 seconds.