The generator matrix

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

generates a code of length 15 over F4[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+261x^32+432x^33+408x^34+456x^35+2265x^36+5184x^37+2208x^38+2400x^39+10146x^40+23328x^41+10896x^42+10800x^43+28419x^44+52800x^45+23712x^46+15456x^47+27894x^48+34992x^49+5784x^50+1608x^51+2607x^52+66x^56+21x^60

The gray image is a linear code over GF(4) with n=60, k=9 and d=32.
This code was found by Heurico 1.16 in 31.2 seconds.