The generator matrix

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

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+138x^168+180x^169+360x^171+375x^172+588x^173+780x^175+612x^176+1092x^177+1068x^179+789x^180+972x^181+1416x^183+729x^184+1452x^185+1488x^187+810x^188+1236x^189+876x^191+414x^192+540x^193+156x^195+99x^196+84x^197+39x^200+24x^204+21x^208+12x^212+18x^216+3x^220+12x^224

The gray image is a linear code over GF(4) with n=244, k=7 and d=168.
This code was found by Heurico 1.16 in 1.36 seconds.