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

generates a code of length 58 over F4[X]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+333x^160+72x^161+144x^163+1095x^164+372x^165+492x^167+1473x^168+456x^169+528x^171+2064x^172+744x^173+936x^175+2382x^176+792x^177+768x^179+1821x^180+516x^181+204x^183+801x^184+120x^185+147x^188+39x^192+33x^196+18x^200+18x^204+9x^208+3x^212+3x^220

The gray image is a linear code over GF(4) with n=232, k=7 and d=160.
This code was found by Heurico 1.16 in 1.3 seconds.