The generator matrix

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

generates a code of length 39 over F4[X]/(X^2) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+192x^110+384x^111+486x^112+432x^114+504x^115+411x^116+192x^118+240x^119+282x^120+144x^122+312x^123+108x^124+192x^126+96x^127+111x^128+9x^132

The gray image is a linear code over GF(4) with n=156, k=6 and d=110.
This code was found by Heurico 1.16 in 0.282 seconds.