The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1
 0  1  1  a a^2  0 a^2*X+1  a a^2*X+a^2  1 a^2*X+1 a^2*X+a^2  0  1  0
 0  0 a^2*X  0  0  X  0 a*X a*X a^2*X a^2*X a*X  X  0  0
 0  0  0  X  0 a^2*X a*X a^2*X  0 a^2*X a^2*X a^2*X  X  X  0
 0  0  0  0 a^2*X  X  X a^2*X a*X a*X  X  0 a^2*X  0  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+39x^32+12x^33+285x^36+144x^37+192x^39+1467x^40+648x^41+1152x^43+4080x^44+1296x^45+1728x^47+4098x^48+972x^49+189x^52+75x^56+6x^60

The gray image is a linear code over GF(4) with n=60, k=7 and d=32.
This code was found by Heurico 1.16 in 0.19 seconds.