The generator matrix

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

generates a code of length 13 over F4[X]/(X^2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+96x^25+204x^27+744x^28+624x^29+1152x^30+2448x^31+2805x^32+5376x^33+10368x^34+11016x^35+17100x^36+24096x^37+31104x^38+25104x^39+36480x^40+34080x^41+31104x^42+16524x^43+8256x^44+3312x^45+138x^48+12x^52

The gray image is a linear code over GF(4) with n=52, k=9 and d=25.
This code was found by Heurico 1.16 in 22.5 seconds.