The generator matrix

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

generates a code of length 59 over F4[X]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+183x^160+240x^161+36x^162+540x^163+1299x^164+1344x^165+228x^166+1368x^167+2904x^168+2628x^169+444x^170+2424x^171+3843x^172+3876x^173+624x^174+2952x^175+5436x^176+4512x^177+636x^178+3564x^179+5550x^180+4920x^181+708x^182+2856x^183+4581x^184+2868x^185+324x^186+1440x^187+1455x^188+996x^189+72x^190+216x^191+246x^192+120x^193+24x^196+42x^200+18x^204+6x^208+3x^212+9x^216

The gray image is a linear code over GF(4) with n=236, k=8 and d=160.
This code was found by Heurico 1.16 in 16.9 seconds.