The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  1  1  1  1  0 X+2  1  1  0 X+2  1  1  1  0  0  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  3 X+1 X+2  3  1  1  0 X+2  1  1 X+1 X+1 X+1  1  1 X+1
 0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  0  0  0  2  0  2  0  2  2  0  2  2  2  2  2  2  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  2  0  2  2  2  0  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  2  2  0  0  2  2  0  0  2  2  0  0  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  0  2  2  2  0  0  2  2  2  0  2  2  2  2  0  2  0  2  2  2  2
 0  0  0  0  0  0  2  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  0  0  0  0  2  0  2  0  0  2  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  0  2  0  0  0  2  2  0  2  2  2  2  2  2  2  2  0  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  0  2  2  0  2  2  0  0  0  2  2  2  2  0  2  2  2  2  2  2  0
 0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  2  0  0  2  2  0  0  2  0  0  2  2  2  2  2

generates a code of length 36 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+53x^26+8x^27+145x^28+24x^29+275x^30+592x^31+495x^32+1840x^33+696x^34+3680x^35+767x^36+3680x^37+707x^38+1840x^39+508x^40+592x^41+266x^42+24x^43+111x^44+8x^45+41x^46+20x^48+8x^50+1x^52+1x^54+1x^58

The gray image is a code over GF(2) with n=144, k=14 and d=52.
This code was found by Heurico 1.16 in 93.1 seconds.