The generator matrix

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

generates a code of length 62 over F4[X]/(X^2) who´s minimum homogenous weight is 167.

Homogenous weight enumerator: w(x)=1x^0+624x^167+759x^168+744x^169+1032x^170+2868x^171+2856x^172+2736x^173+2736x^174+6300x^175+5436x^176+4524x^177+5148x^178+12432x^179+9564x^180+7668x^181+8532x^182+18876x^183+12822x^184+10272x^185+11748x^186+22920x^187+13785x^188+11244x^189+11064x^190+19908x^191+12390x^192+7788x^193+6852x^194+10752x^195+5931x^196+3372x^197+1764x^198+3252x^199+1629x^200+768x^201+276x^202+372x^203+285x^204+36x^205+33x^208+21x^212+15x^216+6x^220+3x^232

The gray image is a linear code over GF(4) with n=248, k=9 and d=167.
This code was found by Heurico 1.16 in 238 seconds.