The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1 a^2*X  1  1  1  0  1  1  1  1  1 a^2*X  X a*X  1  0  0 a^2*X  1  1  1  1  1  1  1  1  1  1  1  1  1  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 a^2  1 a^2*X+a^2  1  1 a^2*X+a^2  a  1 X+a^2  1 a*X+a^2  X a^2*X+a^2  1  0  1 a^2*X+a  1  1  1  a a^2*X+a X+1 a*X a*X+a^2 a*X+a^2 X+a  a a^2*X+a a^2*X+1 a^2*X+1 a^2*X+1 a^2*X+1 a*X X+1 a^2 a*X+1  X  a X+1  a a^2*X+a^2 a*X+a a*X+a  0  1 a*X+a^2
 0  0  1  1  a a^2  1 X+1  1  a  0  X a^2 a*X+a^2 a^2 a*X+a X+1 a^2  0 a*X+a  a a^2*X+1 a^2*X+a  a  a a^2*X X+a^2  1 X+a  1 a^2*X+1 a^2*X+1  X a^2*X a*X+a a*X+1 a^2*X+1 a*X+a^2 a*X+a^2 a*X+a a^2*X X+a a^2*X+a a*X+a^2 a^2*X  0  X a*X+a a^2*X a^2*X+a^2  a  1 a*X+1  0 a^2*X  a a*X+a^2 a^2*X+a^2  X a*X+1
 0  0  0 a^2*X  0  0  0  X  X  X a^2*X a*X a^2*X a*X a^2*X a*X a*X  X a^2*X  X a*X  0 a^2*X  0 a*X  X  0  X  X  0  X a*X  X  X  0  0  X a*X  0  0 a*X a*X  X a^2*X a^2*X  0 a*X  0 a^2*X  X a*X a*X a*X  X  0  X  0 a*X a^2*X  0
 0  0  0  0  X a^2*X a*X  X a^2*X a*X a*X  X  X a*X a*X  0  X a^2*X  X a*X  0  X  0 a^2*X a^2*X a*X a*X  X  0  0 a^2*X a*X  X  0  X  X  0  X  0 a*X a*X a^2*X  X  X  0  X a*X  0 a*X  X a*X a^2*X  0 a^2*X a^2*X a^2*X a^2*X a^2*X  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+585x^164+156x^165+180x^166+528x^167+2619x^168+948x^169+696x^170+1260x^171+4065x^172+1776x^173+804x^174+2280x^175+5826x^176+2304x^177+1224x^178+2400x^179+7368x^180+2652x^181+1356x^182+3072x^183+7200x^184+2868x^185+1272x^186+1932x^187+5016x^188+1368x^189+540x^190+744x^191+1803x^192+216x^193+72x^194+72x^195+216x^196+63x^200+24x^204+18x^208+3x^212+6x^216+3x^220

The gray image is a linear code over GF(4) with n=240, k=8 and d=164.
This code was found by Heurico 1.16 in 18.5 seconds.