The generator matrix

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

generates a code of length 60 over F4[X]/(X^2) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+69x^164+24x^166+228x^167+417x^168+300x^170+804x^171+1080x^172+408x^174+876x^175+1287x^176+648x^178+1344x^179+1410x^180+888x^182+1500x^183+1581x^184+684x^186+996x^187+951x^188+120x^190+372x^191+228x^192+24x^195+36x^196+27x^200+36x^204+18x^208+15x^212+9x^216+3x^220

The gray image is a linear code over GF(4) with n=240, k=7 and d=164.
This code was found by Heurico 1.16 in 1.32 seconds.