The generator matrix

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

generates a code of length 61 over F4[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+375x^168+840x^169+564x^170+888x^171+1452x^172+2604x^173+1344x^174+1464x^175+2736x^176+4056x^177+1944x^178+1920x^179+3327x^180+4956x^181+1800x^182+2088x^183+3636x^184+5892x^185+2340x^186+1992x^187+3510x^188+4884x^189+1776x^190+1752x^191+2082x^192+2352x^193+816x^194+576x^195+675x^196+516x^197+168x^198+72x^199+111x^200+12x^201+12x^204+3x^208

The gray image is a linear code over GF(4) with n=244, k=8 and d=168.
This code was found by Heurico 1.16 in 17.4 seconds.