The generator matrix

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

generates a code of length 12 over F4[X]/(X^2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+132x^25+240x^27+1068x^28+912x^29+864x^30+2160x^31+3306x^32+3768x^33+5184x^34+6480x^35+11220x^36+8400x^37+7776x^38+6480x^39+5358x^40+2148x^41+24x^44+15x^48

The gray image is a linear code over GF(4) with n=48, k=8 and d=25.
This code was found by Heurico 1.16 in 1.67 seconds.