The generator matrix

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

generates a code of length 15 over F4[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+63x^36+36x^37+48x^39+390x^40+180x^41+288x^43+1029x^44+300x^45+432x^47+1017x^48+252x^49+33x^52+24x^56+3x^60

The gray image is a linear code over GF(4) with n=60, k=6 and d=36.
This code was found by Heurico 1.16 in 0.0154 seconds.