The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+20x^20+64x^23+90x^24+64x^25+11x^28+5x^32+1x^44

The gray image is a code over GF(2) with n=96, k=8 and d=40.
This code was found by Heurico 1.16 in 0.00513 seconds.