The generator matrix

 1  0  0  1  1  1  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 a*X+1 a^2*X+a^2 a^2*X  0
 0  0  1 a^2  a  1  a  1 a^2  a a*X+a a*X+a  0  1  0
 0  0  0  X  0  X  0  X a^2*X a^2*X a^2*X a*X a^2*X a*X  X
 0  0  0  0  X a^2*X a*X  X  0 a^2*X  X  X a*X  0 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+81x^32+120x^33+36x^34+312x^35+588x^36+864x^37+288x^38+1248x^39+2784x^40+4752x^41+2376x^42+5328x^43+7668x^44+8928x^45+5760x^46+7392x^47+7686x^48+6840x^49+756x^50+1080x^51+564x^52+72x^56+12x^60

The gray image is a linear code over GF(4) with n=60, k=8 and d=32.
This code was found by Heurico 1.16 in 2.47 seconds.