The generator matrix

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

generates a code of length 52 over F4[X]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+216x^136+393x^140+12x^141+393x^144+180x^145+480x^148+1080x^149+411x^152+3240x^153+453x^156+4860x^157+414x^160+2916x^161+396x^164+318x^168+267x^172+189x^176+108x^180+39x^184+15x^188+3x^192

The gray image is a linear code over GF(4) with n=208, k=7 and d=136.
This code was found by Heurico 1.16 in 34.8 seconds.