The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1
 0  1  1  a a^2  0 a^2*X+1  a a^2*X+a^2  1 a^2*X+1  0
 0  0 a^2*X  0  0  X  0 a*X a*X a^2*X a^2*X  0
 0  0  0  X  0 a^2*X a*X a^2*X  0 a^2*X a^2*X  0
 0  0  0  0 a^2*X  X  X a^2*X a*X a*X  X  0

generates a code of length 12 over F4[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+81x^24+240x^27+135x^28+576x^30+1008x^31+147x^32+3456x^34+1872x^35+222x^36+5184x^38+3024x^39+237x^40+171x^44+30x^48

The gray image is a linear code over GF(4) with n=48, k=7 and d=24.
This code was found by Heurico 1.16 in 0.123 seconds.