The generator matrix

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

generates a code of length 61 over F4[X]/(X^2) who´s minimum homogenous weight is 182.

Homogenous weight enumerator: w(x)=1x^0+108x^182+96x^183+9x^184+36x^186+6x^212

The gray image is a linear code over GF(4) with n=244, k=4 and d=182.
This code was found by Heurico 1.16 in 1.27 seconds.