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

generates a code of length 59 over F4[X]/(X^2) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+96x^162+108x^163+300x^164+192x^165+468x^166+312x^167+420x^168+360x^169+876x^170+396x^171+669x^172+516x^173+1008x^174+648x^175+909x^176+816x^177+1560x^178+708x^179+927x^180+648x^181+1428x^182+552x^183+525x^184+456x^185+540x^186+324x^187+204x^188+84x^189+168x^190+24x^191+27x^192+30x^196+27x^200+18x^204+21x^208+9x^212+6x^216+3x^220

The gray image is a linear code over GF(4) with n=236, k=7 and d=162.
This code was found by Heurico 1.16 in 74.1 seconds.