The generator matrix

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

generates a code of length 61 over F4[X]/(X^2) who´s minimum homogenous weight is 167.

Homogenous weight enumerator: w(x)=1x^0+408x^167+462x^168+228x^169+480x^170+1764x^171+1626x^172+1044x^173+1008x^174+3552x^175+2460x^176+1152x^177+1452x^178+5100x^179+3837x^180+2208x^181+1968x^182+5472x^183+4278x^184+1860x^185+2040x^186+5532x^187+4053x^188+1620x^189+1680x^190+4032x^191+2001x^192+984x^193+540x^194+1620x^195+558x^196+120x^197+48x^198+168x^199+84x^200+33x^204+33x^208+15x^212+6x^216+6x^220+3x^224

The gray image is a linear code over GF(4) with n=244, k=8 and d=167.
This code was found by Heurico 1.16 in 25.6 seconds.