The generator matrix

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

generates a code of length 61 over F4[X]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+348x^176+600x^177+300x^178+672x^180+288x^181+228x^182+294x^184+276x^185+72x^186+213x^188+132x^189+108x^190+123x^192+132x^193+36x^194+72x^196+108x^197+24x^198+63x^200+3x^204+3x^216

The gray image is a linear code over GF(4) with n=244, k=6 and d=176.
This code was found by Heurico 1.16 in 0.296 seconds.