The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 (a+1)X  1  0  1  1  1 (a+1)X aX  1  1  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  1  0  1 aX  1  1  1  1  1  1  1  1  1 aX  1  1 aX  1
 0  1  0  0  0 (a+1)X  1 (a+1)X+a a+1 (a+1)X+1  1 (a+1)X+a  a (a+1)X+a+1  1 (a+1)X+a+1  1 (a+1)X+1 a+1  a  1  1 (a+1)X+a+1  0 a+1  a X+a+1 aX+a+1 aX+a (a+1)X+a (a+1)X  1  X aX+1  a  1 aX  1  a X+a X+a+1 aX (a+1)X+a  1  0 a+1  0 aX+a+1 aX+a  X a+1 aX aX+1  1 a+1 (a+1)X  1 (a+1)X+a
 0  0  1  1  a a+1  1 X+1  1  0 a+1 X+a+1  a aX+a X+1 aX  a  a a+1  X X+a+1  0 X+1 (a+1)X+a X+a+1 X+a X+a  X aX+a+1 (a+1)X+1 X+a+1 (a+1)X+a aX+1 aX  0 (a+1)X+1  1 X+1  X  1  1  1 a+1 X+1 X+a X+a+1 a+1  0  a (a+1)X+1 X+1 aX+a+1 (a+1)X+a (a+1)X+a  1 (a+1)X aX+1 aX
 0  0  0 (a+1)X  0  0  0 aX aX aX (a+1)X  X (a+1)X  X (a+1)X  X  X aX (a+1)X  X aX  0 (a+1)X aX  0 (a+1)X  0  0 aX  0  X  X  X (a+1)X  X  0  X aX  0  0  X (a+1)X aX  0  X aX (a+1)X (a+1)X  0 (a+1)X (a+1)X  X (a+1)X aX  X  X  X (a+1)X
 0  0  0  0  X aX (a+1)X  X  0 aX  X (a+1)X aX  0 (a+1)X  X  X  0 aX  0  X (a+1)X (a+1)X  X  0  0 aX  X aX  X  X (a+1)X aX  0 aX aX  X (a+1)X (a+1)X aX aX  X (a+1)X  X aX aX (a+1)X aX (a+1)X (a+1)X  X (a+1)X (a+1)X  X  0 (a+1)X  X aX

generates a code of length 58 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 157.

Homogenous weight enumerator: w(x)=1x^0+180x^157+216x^158+336x^159+552x^160+1116x^161+816x^162+1068x^163+1341x^164+2232x^165+1848x^166+1632x^167+1866x^168+3384x^169+2688x^170+3120x^171+2754x^172+4620x^173+3600x^174+4032x^175+2985x^176+4716x^177+3408x^178+3516x^179+2220x^180+3456x^181+2136x^182+1392x^183+1215x^184+1536x^185+576x^186+264x^187+261x^188+264x^189+72x^190+27x^192+39x^196+27x^200+6x^204+12x^208+3x^220+3x^224

The gray image is a linear code over GF(4) with n=232, k=8 and d=157.
This code was found by Heurico 1.16 in 40 seconds.