The generator matrix

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

generates a code of length 52 over F4[X]/(X^2) who´s minimum homogenous weight is 142.

Homogenous weight enumerator: w(x)=1x^0+744x^142+1128x^143+297x^144+3720x^146+2460x^147+543x^148+5424x^150+4032x^151+795x^152+7716x^154+5640x^155+744x^156+8700x^158+5808x^159+894x^160+7284x^162+3924x^163+600x^164+2844x^166+1512x^167+189x^168+432x^170+72x^171+24x^172+9x^180

The gray image is a linear code over GF(4) with n=208, k=8 and d=142.
This code was found by Heurico 1.16 in 31.2 seconds.