The generator matrix

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

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+57x^24+120x^25+156x^26+336x^27+465x^28+480x^29+1488x^30+3024x^31+1461x^32+3984x^33+7848x^34+9072x^35+2802x^36+9312x^37+11472x^38+9072x^39+2217x^40+1464x^41+540x^42+141x^44+24x^48

The gray image is a linear code over GF(4) with n=48, k=8 and d=24.
This code was found by Heurico 1.16 in 1.6 seconds.