The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  X  0 a*X a*X  X a^2*X a^2*X  X  0  0
 0  0  X  0  0 a^2*X  X  0 a*X a*X a*X  X a*X  0  X
 0  0  0  X  0  X a^2*X a^2*X a*X  0 a*X  X  0 a^2*X a*X
 0  0  0  0  X a^2*X a*X  X a^2*X  X  0  X a^2*X a^2*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+42x^32+123x^36+189x^40+195x^44+3072x^45+225x^48+153x^52+87x^56+9x^60

The gray image is a linear code over GF(4) with n=60, k=6 and d=32.
This code was found by Heurico 1.16 in 0.0247 seconds.