The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  X a^2*X  1 a^2*X+a a^2  1 a^2 a^2*X+a a^2*X+a^2 a^2*X+1 a*X+1
 0  0  1  1 a^2*X+a a^2 a^2 X+a^2 X+a^2 X+1  1 X+1  a  a a*X+a
 0  0  0 a^2*X a*X a*X  X  X a^2*X a^2*X  X a*X a*X  0 a^2*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+123x^36+156x^37+600x^38+192x^39+807x^40+684x^41+1080x^42+1152x^43+2310x^44+1236x^45+1800x^46+1728x^47+2331x^48+996x^49+1128x^50+39x^52+21x^56

The gray image is a linear code over GF(4) with n=60, k=7 and d=36.
This code was found by Heurico 1.16 in 0.156 seconds.